<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "https://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.9.1"/>
<meta name="viewport" content="width=device-width, initial-scale=1"/>
<title>Doxygen: common/include/pcl/common/impl/eigen.hpp 源文件</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="navtree.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="resize.js"></script>
<script type="text/javascript" src="navtreedata.js"></script>
<script type="text/javascript" src="navtree.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
 <tbody>
 <tr style="height: 56px;">
  <td id="projectalign" style="padding-left: 0.5em;">
   <div id="projectname">Doxygen
   </div>
  </td>
 </tr>
 </tbody>
</table>
</div>
<!-- end header part -->
<!-- 制作者 Doxygen 1.9.1 -->
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
var searchBox = new SearchBox("searchBox", "search",false,'搜索','.html');
/* @license-end */
</script>
<script type="text/javascript" src="menudata.js"></script>
<script type="text/javascript" src="menu.js"></script>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(function() {
  initMenu('',true,false,'search.php','搜索');
  $(document).ready(function() { init_search(); });
});
/* @license-end */</script>
<div id="main-nav"></div>
</div><!-- top -->
<div id="side-nav" class="ui-resizable side-nav-resizable">
  <div id="nav-tree">
    <div id="nav-tree-contents">
      <div id="nav-sync" class="sync"></div>
    </div>
  </div>
  <div id="splitbar" style="-moz-user-select:none;" 
       class="ui-resizable-handle">
  </div>
</div>
<script type="text/javascript">
/* @license magnet:?xt=urn:btih:cf05388f2679ee054f2beb29a391d25f4e673ac3&amp;dn=gpl-2.0.txt GPL-v2 */
$(document).ready(function(){initNavTree('common_2include_2pcl_2common_2impl_2eigen_8hpp_source.html',''); initResizable(); });
/* @license-end */
</script>
<div id="doc-content">
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
     onmouseover="return searchBox.OnSearchSelectShow()"
     onmouseout="return searchBox.OnSearchSelectHide()"
     onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>

<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0" 
        name="MSearchResults" id="MSearchResults">
</iframe>
</div>

<div class="header">
  <div class="headertitle">
<div class="title">eigen.hpp</div>  </div>
</div><!--header-->
<div class="contents">
<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="comment">/*</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment"> * Software License Agreement (BSD License)</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment"> *  Point Cloud Library (PCL) - www.pointclouds.org</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment"> *  Copyright (c) 2010, Willow Garage, Inc.</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"> *  Copyright (c) 2012-, Open Perception, Inc.</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"> *  All rights reserved.</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment"> *  Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment"> *  modification, are permitted provided that the following conditions</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160;<span class="comment"> *  are met:</span></div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment"> *   * Redistributions of source code must retain the above copyright</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment"> *     notice, this list of conditions and the following disclaimer.</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="comment"> *   * Redistributions in binary form must reproduce the above</span></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;<span class="comment"> *     copyright notice, this list of conditions and the following</span></div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="comment"> *     disclaimer in the documentation and/or other materials provided</span></div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="comment"> *     with the distribution.</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="comment"> *   * Neither the name of the copyright holder(s) nor the names of its</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;<span class="comment"> *     contributors may be used to endorse or promote products derived</span></div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="comment"> *     from this software without specific prior written permission.</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;<span class="comment"> *  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS</span></div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="comment"> *  &quot;AS IS&quot; AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="comment"> *  LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;<span class="comment"> *  FOR a PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="comment"> *  COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;<span class="comment"> *  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,</span></div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="comment"> *  BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;</span></div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="comment"> *  LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER</span></div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;<span class="comment"> *  CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT</span></div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;<span class="comment"> *  LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;<span class="comment"> *  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;<span class="comment"> *  POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;<span class="comment"> *</span></div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;<span class="comment"> */</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160; </div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;<span class="preprocessor">#ifndef PCL_COMMON_EIGEN_IMPL_HPP_</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;<span class="preprocessor">#define PCL_COMMON_EIGEN_IMPL_HPP_</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160; </div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;<span class="preprocessor">#include &lt;pcl/console/print.h&gt;</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160; </div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar, <span class="keyword">typename</span> Roots&gt; <span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;pcl::computeRoots2 (<span class="keyword">const</span> Scalar&amp; b, <span class="keyword">const</span> Scalar&amp; c, Roots&amp; roots)</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;{</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;  roots (0) = Scalar (0);</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  Scalar d = Scalar (b * b - 4.0 * c);</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  <span class="keywordflow">if</span> (d &lt; 0.0)  <span class="comment">// no real roots ! THIS SHOULD NOT HAPPEN!</span></div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;    d = 0.0;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;  Scalar sd = ::std::sqrt (d);</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160; </div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;  roots (2) = 0.5f * (b + sd);</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;  roots (1) = 0.5f * (b - sd);</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;}</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix, <span class="keyword">typename</span> Roots&gt; <span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;pcl::computeRoots (<span class="keyword">const</span> Matrix&amp; m, Roots&amp; roots)</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;{</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix::Scalar Scalar;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160; </div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;  <span class="comment">// The characteristic equation is x^3 - c2*x^2 + c1*x - c0 = 0.  The</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  <span class="comment">// eigenvalues are the roots to this equation, all guaranteed to be</span></div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  <span class="comment">// real-valued, because the matrix is symmetric.</span></div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;  Scalar c0 =      m (0, 0) * m (1, 1) * m (2, 2)</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;      + Scalar (2) * m (0, 1) * m (0, 2) * m (1, 2)</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;             - m (0, 0) * m (1, 2) * m (1, 2)</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;             - m (1, 1) * m (0, 2) * m (0, 2)</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;             - m (2, 2) * m (0, 1) * m (0, 1);</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;  Scalar c1 = m (0, 0) * m (1, 1) -</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;        m (0, 1) * m (0, 1) +</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;        m (0, 0) * m (2, 2) -</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;        m (0, 2) * m (0, 2) +</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;        m (1, 1) * m (2, 2) -</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;        m (1, 2) * m (1, 2);</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;  Scalar c2 = m (0, 0) + m (1, 1) + m (2, 2);</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160; </div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  <span class="keywordflow">if</span> (fabs (c0) &lt; Eigen::NumTraits &lt; Scalar &gt; ::epsilon ())  <span class="comment">// one root is 0 -&gt; quadratic equation</span></div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;    computeRoots2 (c2, c1, roots);</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  {</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;    <span class="keyword">const</span> Scalar s_inv3 = Scalar (1.0 / 3.0);</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;    <span class="keyword">const</span> Scalar s_sqrt3 = std::sqrt (Scalar (3.0));</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;    <span class="comment">// Construct the parameters used in classifying the roots of the equation</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;    <span class="comment">// and in solving the equation for the roots in closed form.</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;    Scalar c2_over_3 = c2 * s_inv3;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;    Scalar a_over_3 = (c1 - c2 * c2_over_3) * s_inv3;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;    <span class="keywordflow">if</span> (a_over_3 &gt; Scalar (0))</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;      a_over_3 = Scalar (0);</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;    Scalar half_b = Scalar (0.5) * (c0 + c2_over_3 * (Scalar (2) * c2_over_3 * c2_over_3 - c1));</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160; </div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;    Scalar q = half_b * half_b + a_over_3 * a_over_3 * a_over_3;</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;    <span class="keywordflow">if</span> (q &gt; Scalar (0))</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;      q = Scalar (0);</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;    <span class="comment">// Compute the eigenvalues by solving for the roots of the polynomial.</span></div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;    Scalar rho = std::sqrt (-a_over_3);</div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;    Scalar theta = std::atan2 (std::sqrt (-q), half_b) * s_inv3;</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;    Scalar cos_theta = std::cos (theta);</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;    Scalar sin_theta = std::sin (theta);</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;    roots (0) = c2_over_3 + Scalar (2) * rho * cos_theta;</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;    roots (1) = c2_over_3 - rho * (cos_theta + s_sqrt3 * sin_theta);</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;    roots (2) = c2_over_3 - rho * (cos_theta - s_sqrt3 * sin_theta);</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160; </div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;    <span class="comment">// Sort in increasing order.</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;    <span class="keywordflow">if</span> (roots (0) &gt;= roots (1))</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;      std::swap (roots (0), roots (1));</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;    <span class="keywordflow">if</span> (roots (1) &gt;= roots (2))</div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;    {</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;      std::swap (roots (1), roots (2));</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;      <span class="keywordflow">if</span> (roots (0) &gt;= roots (1))</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;        std::swap (roots (0), roots (1));</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;    }</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160; </div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;    <span class="keywordflow">if</span> (roots (0) &lt;= 0)  <span class="comment">// eigenval for symetric positive semi-definite matrix can not be negative! Set it to 0</span></div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;      computeRoots2 (c2, c1, roots);</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  }</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;}</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160; </div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix, <span class="keyword">typename</span> Vector&gt; <span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"><a class="line" href="group__common.html#ga72970b7435480c0c1827c8e74bc1d605">  126</a></span>&#160;<a class="code" href="group__common.html#ga72970b7435480c0c1827c8e74bc1d605">pcl::eigen22</a> (<span class="keyword">const</span> Matrix&amp; mat, <span class="keyword">typename</span> Matrix::Scalar&amp; eigenvalue, Vector&amp; eigenvector)</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;{</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;  <span class="comment">// if diagonal matrix, the eigenvalues are the diagonal elements</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;  <span class="comment">// and the eigenvectors are not unique, thus set to Identity</span></div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;  <span class="keywordflow">if</span> (fabs (mat.coeff (1)) &lt;= std::numeric_limits&lt;typename Matrix::Scalar&gt;::min ())</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;  {</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;    <span class="keywordflow">if</span> (mat.coeff (0) &lt; mat.coeff (2))</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;    {</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;      eigenvalue = mat.coeff (0);</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;      eigenvector[0] = 1.0;</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;      eigenvector[1] = 0.0;</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;    }</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;    {</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;      eigenvalue = mat.coeff (2);</div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;      eigenvector[0] = 0.0;</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;      eigenvector[1] = 1.0;</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;    }</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;  }</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160; </div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;  <span class="comment">// 0.5 to optimize further calculations</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;  <span class="keyword">typename</span> Matrix::Scalar trace = <span class="keyword">static_cast&lt;</span>typename Matrix::Scalar<span class="keyword">&gt;</span> (0.5) * (mat.coeff (0) + mat.coeff (3));</div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;  <span class="keyword">typename</span> Matrix::Scalar determinant = mat.coeff (0) * mat.coeff (3) - mat.coeff (1) * mat.coeff (1);</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160; </div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;  <span class="keyword">typename</span> Matrix::Scalar temp = trace * trace - determinant;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160; </div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;  <span class="keywordflow">if</span> (temp &lt; 0)</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;    temp = 0;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160; </div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;  eigenvalue = trace - ::std::sqrt (temp);</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160; </div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;  eigenvector[0] = -mat.coeff (1);</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;  eigenvector[1] = mat.coeff (0) - eigenvalue;</div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;  eigenvector.normalize ();</div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;}</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160; </div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix, <span class="keyword">typename</span> Vector&gt; <span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"><a class="line" href="group__common.html#ga4fdd69805d49c416393c604f9f209113">  165</a></span>&#160;<a class="code" href="group__common.html#ga72970b7435480c0c1827c8e74bc1d605">pcl::eigen22</a> (<span class="keyword">const</span> Matrix&amp; mat, Matrix&amp; eigenvectors, Vector&amp; eigenvalues)</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;{</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;  <span class="comment">// if diagonal matrix, the eigenvalues are the diagonal elements</span></div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;  <span class="comment">// and the eigenvectors are not unique, thus set to Identity</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;  <span class="keywordflow">if</span> (fabs (mat.coeff (1)) &lt;= std::numeric_limits&lt;typename Matrix::Scalar&gt;::min ())</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;  {</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;    <span class="keywordflow">if</span> (mat.coeff (0) &lt; mat.coeff (3))</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;    {</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;      eigenvalues.coeffRef (0) = mat.coeff (0);</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;      eigenvalues.coeffRef (1) = mat.coeff (3);</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;      eigenvectors.coeffRef (0) = 1.0;</div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;      eigenvectors.coeffRef (1) = 0.0;</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;      eigenvectors.coeffRef (2) = 0.0;</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;      eigenvectors.coeffRef (3) = 1.0;</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;    }</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    {</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;      eigenvalues.coeffRef (0) = mat.coeff (3);</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;      eigenvalues.coeffRef (1) = mat.coeff (0);</div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;      eigenvectors.coeffRef (0) = 0.0;</div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;      eigenvectors.coeffRef (1) = 1.0;</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;      eigenvectors.coeffRef (2) = 1.0;</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;      eigenvectors.coeffRef (3) = 0.0;</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;    }</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;    <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;  }</div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160; </div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;  <span class="comment">// 0.5 to optimize further calculations</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;  <span class="keyword">typename</span> Matrix::Scalar trace = <span class="keyword">static_cast&lt;</span>typename Matrix::Scalar<span class="keyword">&gt;</span> (0.5) * (mat.coeff (0) + mat.coeff (3));</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;  <span class="keyword">typename</span> Matrix::Scalar determinant = mat.coeff (0) * mat.coeff (3) - mat.coeff (1) * mat.coeff (1);</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160; </div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;  <span class="keyword">typename</span> Matrix::Scalar temp = trace * trace - determinant;</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160; </div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;  <span class="keywordflow">if</span> (temp &lt; 0)</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;    temp = 0;</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;    temp = ::std::sqrt (temp);</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160; </div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;  eigenvalues.coeffRef (0) = trace - temp;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;  eigenvalues.coeffRef (1) = trace + temp;</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160; </div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;  <span class="comment">// either this is in a row or column depending on RowMajor or ColumnMajor</span></div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;  eigenvectors.coeffRef (0) = -mat.coeff (1);</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;  eigenvectors.coeffRef (2) = mat.coeff (0) - eigenvalues.coeff (0);</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;  <span class="keyword">typename</span> Matrix::Scalar norm = <span class="keyword">static_cast&lt;</span>typename Matrix::Scalar<span class="keyword">&gt;</span> (1.0)</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;      / <span class="keyword">static_cast&lt;</span>typename Matrix::Scalar<span class="keyword">&gt;</span> (::std::sqrt (eigenvectors.coeffRef (0) * eigenvectors.coeffRef (0) + eigenvectors.coeffRef (2) * eigenvectors.coeffRef (2)));</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;  eigenvectors.coeffRef (0) *= norm;</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;  eigenvectors.coeffRef (2) *= norm;</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;  eigenvectors.coeffRef (1) = eigenvectors.coeffRef (2);</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;  eigenvectors.coeffRef (3) = -eigenvectors.coeffRef (0);</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;}</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160; </div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix, <span class="keyword">typename</span> Vector&gt; <span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00219"></a><span class="lineno"><a class="line" href="group__common.html#ga11c9b186d04d2e8a868e058473214622">  219</a></span>&#160;<a class="code" href="group__common.html#ga11c9b186d04d2e8a868e058473214622">pcl::computeCorrespondingEigenVector</a> (<span class="keyword">const</span> Matrix&amp; mat, <span class="keyword">const</span> <span class="keyword">typename</span> Matrix::Scalar&amp; eigenvalue, Vector&amp; eigenvector)</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;{</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix::Scalar Scalar;</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;  <span class="comment">// Scale the matrix so its entries are in [-1,1].  The scaling is applied</span></div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;  <span class="comment">// only when at least one matrix entry has magnitude larger than 1.</span></div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160; </div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;  Scalar scale = mat.cwiseAbs ().maxCoeff ();</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;  <span class="keywordflow">if</span> (scale &lt;= std::numeric_limits &lt; Scalar &gt; ::min ())</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;    scale = Scalar (1.0);</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160; </div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;  Matrix scaledMat = mat / scale;</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160; </div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;  scaledMat.diagonal ().array () -= eigenvalue / scale;</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160; </div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;  Vector vec1 = scaledMat.row (0).cross (scaledMat.row (1));</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;  Vector vec2 = scaledMat.row (0).cross (scaledMat.row (2));</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;  Vector vec3 = scaledMat.row (1).cross (scaledMat.row (2));</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160; </div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;  Scalar len1 = vec1.squaredNorm ();</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;  Scalar len2 = vec2.squaredNorm ();</div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;  Scalar len3 = vec3.squaredNorm ();</div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160; </div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;  <span class="keywordflow">if</span> (len1 &gt;= len2 &amp;&amp; len1 &gt;= len3)</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;    eigenvector = vec1 / std::sqrt (len1);</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len2 &gt;= len1 &amp;&amp; len2 &gt;= len3)</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;    eigenvector = vec2 / std::sqrt (len2);</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;    eigenvector = vec3 / std::sqrt (len3);</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;}</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160; </div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix, <span class="keyword">typename</span> Vector&gt; <span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00251"></a><span class="lineno"><a class="line" href="group__common.html#gaca873868052e7d26efcf4b684a17bef2">  251</a></span>&#160;<a class="code" href="group__common.html#gaca873868052e7d26efcf4b684a17bef2">pcl::eigen33</a> (<span class="keyword">const</span> Matrix&amp; mat, <span class="keyword">typename</span> Matrix::Scalar&amp; eigenvalue, Vector&amp; eigenvector)</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;{</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix::Scalar Scalar;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;  <span class="comment">// Scale the matrix so its entries are in [-1,1].  The scaling is applied</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;  <span class="comment">// only when at least one matrix entry has magnitude larger than 1.</span></div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160; </div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;  Scalar scale = mat.cwiseAbs ().maxCoeff ();</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;  <span class="keywordflow">if</span> (scale &lt;= std::numeric_limits &lt; Scalar &gt; ::min ())</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;    scale = Scalar (1.0);</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160; </div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;  Matrix scaledMat = mat / scale;</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160; </div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;  Vector eigenvalues;</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;  computeRoots (scaledMat, eigenvalues);</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160; </div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;  eigenvalue = eigenvalues (0) * scale;</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160; </div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;  scaledMat.diagonal ().array () -= eigenvalues (0);</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160; </div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;  Vector vec1 = scaledMat.row (0).cross (scaledMat.row (1));</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;  Vector vec2 = scaledMat.row (0).cross (scaledMat.row (2));</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;  Vector vec3 = scaledMat.row (1).cross (scaledMat.row (2));</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160; </div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;  Scalar len1 = vec1.squaredNorm ();</div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;  Scalar len2 = vec2.squaredNorm ();</div>
<div class="line"><a name="l00276"></a><span class="lineno">  276</span>&#160;  Scalar len3 = vec3.squaredNorm ();</div>
<div class="line"><a name="l00277"></a><span class="lineno">  277</span>&#160; </div>
<div class="line"><a name="l00278"></a><span class="lineno">  278</span>&#160;  <span class="keywordflow">if</span> (len1 &gt;= len2 &amp;&amp; len1 &gt;= len3)</div>
<div class="line"><a name="l00279"></a><span class="lineno">  279</span>&#160;    eigenvector = vec1 / std::sqrt (len1);</div>
<div class="line"><a name="l00280"></a><span class="lineno">  280</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len2 &gt;= len1 &amp;&amp; len2 &gt;= len3)</div>
<div class="line"><a name="l00281"></a><span class="lineno">  281</span>&#160;    eigenvector = vec2 / std::sqrt (len2);</div>
<div class="line"><a name="l00282"></a><span class="lineno">  282</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00283"></a><span class="lineno">  283</span>&#160;    eigenvector = vec3 / std::sqrt (len3);</div>
<div class="line"><a name="l00284"></a><span class="lineno">  284</span>&#160;}</div>
<div class="line"><a name="l00285"></a><span class="lineno">  285</span>&#160; </div>
<div class="line"><a name="l00287"></a><span class="lineno">  287</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix, <span class="keyword">typename</span> Vector&gt; <span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00288"></a><span class="lineno"><a class="line" href="group__common.html#ga3a1ba2729012164635113224cb211581">  288</a></span>&#160;<a class="code" href="group__common.html#gaca873868052e7d26efcf4b684a17bef2">pcl::eigen33</a> (<span class="keyword">const</span> Matrix&amp; mat, Vector&amp; evals)</div>
<div class="line"><a name="l00289"></a><span class="lineno">  289</span>&#160;{</div>
<div class="line"><a name="l00290"></a><span class="lineno">  290</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix::Scalar Scalar;</div>
<div class="line"><a name="l00291"></a><span class="lineno">  291</span>&#160;  Scalar scale = mat.cwiseAbs ().maxCoeff ();</div>
<div class="line"><a name="l00292"></a><span class="lineno">  292</span>&#160;  <span class="keywordflow">if</span> (scale &lt;= std::numeric_limits &lt; Scalar &gt; ::min ())</div>
<div class="line"><a name="l00293"></a><span class="lineno">  293</span>&#160;    scale = Scalar (1.0);</div>
<div class="line"><a name="l00294"></a><span class="lineno">  294</span>&#160; </div>
<div class="line"><a name="l00295"></a><span class="lineno">  295</span>&#160;  Matrix scaledMat = mat / scale;</div>
<div class="line"><a name="l00296"></a><span class="lineno">  296</span>&#160;  computeRoots (scaledMat, evals);</div>
<div class="line"><a name="l00297"></a><span class="lineno">  297</span>&#160;  evals *= scale;</div>
<div class="line"><a name="l00298"></a><span class="lineno">  298</span>&#160;}</div>
<div class="line"><a name="l00299"></a><span class="lineno">  299</span>&#160; </div>
<div class="line"><a name="l00301"></a><span class="lineno">  301</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix, <span class="keyword">typename</span> Vector&gt; <span class="keyword">inline</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00302"></a><span class="lineno"><a class="line" href="group__common.html#ga76d78c3e9c0f3f58a0806499ae6ed97b">  302</a></span>&#160;<a class="code" href="group__common.html#gaca873868052e7d26efcf4b684a17bef2">pcl::eigen33</a> (<span class="keyword">const</span> Matrix&amp; mat, Matrix&amp; evecs, Vector&amp; evals)</div>
<div class="line"><a name="l00303"></a><span class="lineno">  303</span>&#160;{</div>
<div class="line"><a name="l00304"></a><span class="lineno">  304</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix::Scalar Scalar;</div>
<div class="line"><a name="l00305"></a><span class="lineno">  305</span>&#160;  <span class="comment">// Scale the matrix so its entries are in [-1,1].  The scaling is applied</span></div>
<div class="line"><a name="l00306"></a><span class="lineno">  306</span>&#160;  <span class="comment">// only when at least one matrix entry has magnitude larger than 1.</span></div>
<div class="line"><a name="l00307"></a><span class="lineno">  307</span>&#160; </div>
<div class="line"><a name="l00308"></a><span class="lineno">  308</span>&#160;  Scalar scale = mat.cwiseAbs ().maxCoeff ();</div>
<div class="line"><a name="l00309"></a><span class="lineno">  309</span>&#160;  <span class="keywordflow">if</span> (scale &lt;= std::numeric_limits &lt; Scalar &gt; ::min ())</div>
<div class="line"><a name="l00310"></a><span class="lineno">  310</span>&#160;    scale = Scalar (1.0);</div>
<div class="line"><a name="l00311"></a><span class="lineno">  311</span>&#160; </div>
<div class="line"><a name="l00312"></a><span class="lineno">  312</span>&#160;  Matrix scaledMat = mat / scale;</div>
<div class="line"><a name="l00313"></a><span class="lineno">  313</span>&#160; </div>
<div class="line"><a name="l00314"></a><span class="lineno">  314</span>&#160;  <span class="comment">// Compute the eigenvalues</span></div>
<div class="line"><a name="l00315"></a><span class="lineno">  315</span>&#160;  computeRoots (scaledMat, evals);</div>
<div class="line"><a name="l00316"></a><span class="lineno">  316</span>&#160; </div>
<div class="line"><a name="l00317"></a><span class="lineno">  317</span>&#160;  <span class="keywordflow">if</span> ( (evals (2) - evals (0)) &lt;= Eigen::NumTraits &lt; Scalar &gt; ::epsilon ())</div>
<div class="line"><a name="l00318"></a><span class="lineno">  318</span>&#160;  {</div>
<div class="line"><a name="l00319"></a><span class="lineno">  319</span>&#160;    <span class="comment">// all three equal</span></div>
<div class="line"><a name="l00320"></a><span class="lineno">  320</span>&#160;    evecs.setIdentity ();</div>
<div class="line"><a name="l00321"></a><span class="lineno">  321</span>&#160;  }</div>
<div class="line"><a name="l00322"></a><span class="lineno">  322</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( (evals (1) - evals (0)) &lt;= Eigen::NumTraits &lt; Scalar &gt; ::epsilon ())</div>
<div class="line"><a name="l00323"></a><span class="lineno">  323</span>&#160;  {</div>
<div class="line"><a name="l00324"></a><span class="lineno">  324</span>&#160;    <span class="comment">// first and second equal</span></div>
<div class="line"><a name="l00325"></a><span class="lineno">  325</span>&#160;    Matrix tmp;</div>
<div class="line"><a name="l00326"></a><span class="lineno">  326</span>&#160;    tmp = scaledMat;</div>
<div class="line"><a name="l00327"></a><span class="lineno">  327</span>&#160;    tmp.diagonal ().array () -= evals (2);</div>
<div class="line"><a name="l00328"></a><span class="lineno">  328</span>&#160; </div>
<div class="line"><a name="l00329"></a><span class="lineno">  329</span>&#160;    Vector vec1 = tmp.row (0).cross (tmp.row (1));</div>
<div class="line"><a name="l00330"></a><span class="lineno">  330</span>&#160;    Vector vec2 = tmp.row (0).cross (tmp.row (2));</div>
<div class="line"><a name="l00331"></a><span class="lineno">  331</span>&#160;    Vector vec3 = tmp.row (1).cross (tmp.row (2));</div>
<div class="line"><a name="l00332"></a><span class="lineno">  332</span>&#160; </div>
<div class="line"><a name="l00333"></a><span class="lineno">  333</span>&#160;    Scalar len1 = vec1.squaredNorm ();</div>
<div class="line"><a name="l00334"></a><span class="lineno">  334</span>&#160;    Scalar len2 = vec2.squaredNorm ();</div>
<div class="line"><a name="l00335"></a><span class="lineno">  335</span>&#160;    Scalar len3 = vec3.squaredNorm ();</div>
<div class="line"><a name="l00336"></a><span class="lineno">  336</span>&#160; </div>
<div class="line"><a name="l00337"></a><span class="lineno">  337</span>&#160;    <span class="keywordflow">if</span> (len1 &gt;= len2 &amp;&amp; len1 &gt;= len3)</div>
<div class="line"><a name="l00338"></a><span class="lineno">  338</span>&#160;      evecs.col (2) = vec1 / std::sqrt (len1);</div>
<div class="line"><a name="l00339"></a><span class="lineno">  339</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len2 &gt;= len1 &amp;&amp; len2 &gt;= len3)</div>
<div class="line"><a name="l00340"></a><span class="lineno">  340</span>&#160;      evecs.col (2) = vec2 / std::sqrt (len2);</div>
<div class="line"><a name="l00341"></a><span class="lineno">  341</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00342"></a><span class="lineno">  342</span>&#160;      evecs.col (2) = vec3 / std::sqrt (len3);</div>
<div class="line"><a name="l00343"></a><span class="lineno">  343</span>&#160; </div>
<div class="line"><a name="l00344"></a><span class="lineno">  344</span>&#160;    evecs.col (1) = evecs.col (2).unitOrthogonal ();</div>
<div class="line"><a name="l00345"></a><span class="lineno">  345</span>&#160;    evecs.col (0) = evecs.col (1).cross (evecs.col (2));</div>
<div class="line"><a name="l00346"></a><span class="lineno">  346</span>&#160;  }</div>
<div class="line"><a name="l00347"></a><span class="lineno">  347</span>&#160;  <span class="keywordflow">else</span> <span class="keywordflow">if</span> ( (evals (2) - evals (1)) &lt;= Eigen::NumTraits &lt; Scalar &gt; ::epsilon ())</div>
<div class="line"><a name="l00348"></a><span class="lineno">  348</span>&#160;  {</div>
<div class="line"><a name="l00349"></a><span class="lineno">  349</span>&#160;    <span class="comment">// second and third equal</span></div>
<div class="line"><a name="l00350"></a><span class="lineno">  350</span>&#160;    Matrix tmp;</div>
<div class="line"><a name="l00351"></a><span class="lineno">  351</span>&#160;    tmp = scaledMat;</div>
<div class="line"><a name="l00352"></a><span class="lineno">  352</span>&#160;    tmp.diagonal ().array () -= evals (0);</div>
<div class="line"><a name="l00353"></a><span class="lineno">  353</span>&#160; </div>
<div class="line"><a name="l00354"></a><span class="lineno">  354</span>&#160;    Vector vec1 = tmp.row (0).cross (tmp.row (1));</div>
<div class="line"><a name="l00355"></a><span class="lineno">  355</span>&#160;    Vector vec2 = tmp.row (0).cross (tmp.row (2));</div>
<div class="line"><a name="l00356"></a><span class="lineno">  356</span>&#160;    Vector vec3 = tmp.row (1).cross (tmp.row (2));</div>
<div class="line"><a name="l00357"></a><span class="lineno">  357</span>&#160; </div>
<div class="line"><a name="l00358"></a><span class="lineno">  358</span>&#160;    Scalar len1 = vec1.squaredNorm ();</div>
<div class="line"><a name="l00359"></a><span class="lineno">  359</span>&#160;    Scalar len2 = vec2.squaredNorm ();</div>
<div class="line"><a name="l00360"></a><span class="lineno">  360</span>&#160;    Scalar len3 = vec3.squaredNorm ();</div>
<div class="line"><a name="l00361"></a><span class="lineno">  361</span>&#160; </div>
<div class="line"><a name="l00362"></a><span class="lineno">  362</span>&#160;    <span class="keywordflow">if</span> (len1 &gt;= len2 &amp;&amp; len1 &gt;= len3)</div>
<div class="line"><a name="l00363"></a><span class="lineno">  363</span>&#160;      evecs.col (0) = vec1 / std::sqrt (len1);</div>
<div class="line"><a name="l00364"></a><span class="lineno">  364</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len2 &gt;= len1 &amp;&amp; len2 &gt;= len3)</div>
<div class="line"><a name="l00365"></a><span class="lineno">  365</span>&#160;      evecs.col (0) = vec2 / std::sqrt (len2);</div>
<div class="line"><a name="l00366"></a><span class="lineno">  366</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00367"></a><span class="lineno">  367</span>&#160;      evecs.col (0) = vec3 / std::sqrt (len3);</div>
<div class="line"><a name="l00368"></a><span class="lineno">  368</span>&#160; </div>
<div class="line"><a name="l00369"></a><span class="lineno">  369</span>&#160;    evecs.col (1) = evecs.col (0).unitOrthogonal ();</div>
<div class="line"><a name="l00370"></a><span class="lineno">  370</span>&#160;    evecs.col (2) = evecs.col (0).cross (evecs.col (1));</div>
<div class="line"><a name="l00371"></a><span class="lineno">  371</span>&#160;  }</div>
<div class="line"><a name="l00372"></a><span class="lineno">  372</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00373"></a><span class="lineno">  373</span>&#160;  {</div>
<div class="line"><a name="l00374"></a><span class="lineno">  374</span>&#160;    Matrix tmp;</div>
<div class="line"><a name="l00375"></a><span class="lineno">  375</span>&#160;    tmp = scaledMat;</div>
<div class="line"><a name="l00376"></a><span class="lineno">  376</span>&#160;    tmp.diagonal ().array () -= evals (2);</div>
<div class="line"><a name="l00377"></a><span class="lineno">  377</span>&#160; </div>
<div class="line"><a name="l00378"></a><span class="lineno">  378</span>&#160;    Vector vec1 = tmp.row (0).cross (tmp.row (1));</div>
<div class="line"><a name="l00379"></a><span class="lineno">  379</span>&#160;    Vector vec2 = tmp.row (0).cross (tmp.row (2));</div>
<div class="line"><a name="l00380"></a><span class="lineno">  380</span>&#160;    Vector vec3 = tmp.row (1).cross (tmp.row (2));</div>
<div class="line"><a name="l00381"></a><span class="lineno">  381</span>&#160; </div>
<div class="line"><a name="l00382"></a><span class="lineno">  382</span>&#160;    Scalar len1 = vec1.squaredNorm ();</div>
<div class="line"><a name="l00383"></a><span class="lineno">  383</span>&#160;    Scalar len2 = vec2.squaredNorm ();</div>
<div class="line"><a name="l00384"></a><span class="lineno">  384</span>&#160;    Scalar len3 = vec3.squaredNorm ();</div>
<div class="line"><a name="l00385"></a><span class="lineno">  385</span>&#160;<span class="preprocessor">#ifdef _WIN32</span></div>
<div class="line"><a name="l00386"></a><span class="lineno">  386</span>&#160;    Scalar *mmax = <span class="keyword">new</span> Scalar[3];</div>
<div class="line"><a name="l00387"></a><span class="lineno">  387</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00388"></a><span class="lineno">  388</span>&#160;    Scalar mmax[3];</div>
<div class="line"><a name="l00389"></a><span class="lineno">  389</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00390"></a><span class="lineno">  390</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> min_el = 2;</div>
<div class="line"><a name="l00391"></a><span class="lineno">  391</span>&#160;    <span class="keywordtype">unsigned</span> <span class="keywordtype">int</span> max_el = 2;</div>
<div class="line"><a name="l00392"></a><span class="lineno">  392</span>&#160;    <span class="keywordflow">if</span> (len1 &gt;= len2 &amp;&amp; len1 &gt;= len3)</div>
<div class="line"><a name="l00393"></a><span class="lineno">  393</span>&#160;    {</div>
<div class="line"><a name="l00394"></a><span class="lineno">  394</span>&#160;      mmax[2] = len1;</div>
<div class="line"><a name="l00395"></a><span class="lineno">  395</span>&#160;      evecs.col (2) = vec1 / std::sqrt (len1);</div>
<div class="line"><a name="l00396"></a><span class="lineno">  396</span>&#160;    }</div>
<div class="line"><a name="l00397"></a><span class="lineno">  397</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len2 &gt;= len1 &amp;&amp; len2 &gt;= len3)</div>
<div class="line"><a name="l00398"></a><span class="lineno">  398</span>&#160;    {</div>
<div class="line"><a name="l00399"></a><span class="lineno">  399</span>&#160;      mmax[2] = len2;</div>
<div class="line"><a name="l00400"></a><span class="lineno">  400</span>&#160;      evecs.col (2) = vec2 / std::sqrt (len2);</div>
<div class="line"><a name="l00401"></a><span class="lineno">  401</span>&#160;    }</div>
<div class="line"><a name="l00402"></a><span class="lineno">  402</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00403"></a><span class="lineno">  403</span>&#160;    {</div>
<div class="line"><a name="l00404"></a><span class="lineno">  404</span>&#160;      mmax[2] = len3;</div>
<div class="line"><a name="l00405"></a><span class="lineno">  405</span>&#160;      evecs.col (2) = vec3 / std::sqrt (len3);</div>
<div class="line"><a name="l00406"></a><span class="lineno">  406</span>&#160;    }</div>
<div class="line"><a name="l00407"></a><span class="lineno">  407</span>&#160; </div>
<div class="line"><a name="l00408"></a><span class="lineno">  408</span>&#160;    tmp = scaledMat;</div>
<div class="line"><a name="l00409"></a><span class="lineno">  409</span>&#160;    tmp.diagonal ().array () -= evals (1);</div>
<div class="line"><a name="l00410"></a><span class="lineno">  410</span>&#160; </div>
<div class="line"><a name="l00411"></a><span class="lineno">  411</span>&#160;    vec1 = tmp.row (0).cross (tmp.row (1));</div>
<div class="line"><a name="l00412"></a><span class="lineno">  412</span>&#160;    vec2 = tmp.row (0).cross (tmp.row (2));</div>
<div class="line"><a name="l00413"></a><span class="lineno">  413</span>&#160;    vec3 = tmp.row (1).cross (tmp.row (2));</div>
<div class="line"><a name="l00414"></a><span class="lineno">  414</span>&#160; </div>
<div class="line"><a name="l00415"></a><span class="lineno">  415</span>&#160;    len1 = vec1.squaredNorm ();</div>
<div class="line"><a name="l00416"></a><span class="lineno">  416</span>&#160;    len2 = vec2.squaredNorm ();</div>
<div class="line"><a name="l00417"></a><span class="lineno">  417</span>&#160;    len3 = vec3.squaredNorm ();</div>
<div class="line"><a name="l00418"></a><span class="lineno">  418</span>&#160;    <span class="keywordflow">if</span> (len1 &gt;= len2 &amp;&amp; len1 &gt;= len3)</div>
<div class="line"><a name="l00419"></a><span class="lineno">  419</span>&#160;    {</div>
<div class="line"><a name="l00420"></a><span class="lineno">  420</span>&#160;      mmax[1] = len1;</div>
<div class="line"><a name="l00421"></a><span class="lineno">  421</span>&#160;      evecs.col (1) = vec1 / std::sqrt (len1);</div>
<div class="line"><a name="l00422"></a><span class="lineno">  422</span>&#160;      min_el = len1 &lt;= mmax[min_el] ? 1 : min_el;</div>
<div class="line"><a name="l00423"></a><span class="lineno">  423</span>&#160;      max_el = len1 &gt; mmax[max_el] ? 1 : max_el;</div>
<div class="line"><a name="l00424"></a><span class="lineno">  424</span>&#160;    }</div>
<div class="line"><a name="l00425"></a><span class="lineno">  425</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len2 &gt;= len1 &amp;&amp; len2 &gt;= len3)</div>
<div class="line"><a name="l00426"></a><span class="lineno">  426</span>&#160;    {</div>
<div class="line"><a name="l00427"></a><span class="lineno">  427</span>&#160;      mmax[1] = len2;</div>
<div class="line"><a name="l00428"></a><span class="lineno">  428</span>&#160;      evecs.col (1) = vec2 / std::sqrt (len2);</div>
<div class="line"><a name="l00429"></a><span class="lineno">  429</span>&#160;      min_el = len2 &lt;= mmax[min_el] ? 1 : min_el;</div>
<div class="line"><a name="l00430"></a><span class="lineno">  430</span>&#160;      max_el = len2 &gt; mmax[max_el] ? 1 : max_el;</div>
<div class="line"><a name="l00431"></a><span class="lineno">  431</span>&#160;    }</div>
<div class="line"><a name="l00432"></a><span class="lineno">  432</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00433"></a><span class="lineno">  433</span>&#160;    {</div>
<div class="line"><a name="l00434"></a><span class="lineno">  434</span>&#160;      mmax[1] = len3;</div>
<div class="line"><a name="l00435"></a><span class="lineno">  435</span>&#160;      evecs.col (1) = vec3 / std::sqrt (len3);</div>
<div class="line"><a name="l00436"></a><span class="lineno">  436</span>&#160;      min_el = len3 &lt;= mmax[min_el] ? 1 : min_el;</div>
<div class="line"><a name="l00437"></a><span class="lineno">  437</span>&#160;      max_el = len3 &gt; mmax[max_el] ? 1 : max_el;</div>
<div class="line"><a name="l00438"></a><span class="lineno">  438</span>&#160;    }</div>
<div class="line"><a name="l00439"></a><span class="lineno">  439</span>&#160; </div>
<div class="line"><a name="l00440"></a><span class="lineno">  440</span>&#160;    tmp = scaledMat;</div>
<div class="line"><a name="l00441"></a><span class="lineno">  441</span>&#160;    tmp.diagonal ().array () -= evals (0);</div>
<div class="line"><a name="l00442"></a><span class="lineno">  442</span>&#160; </div>
<div class="line"><a name="l00443"></a><span class="lineno">  443</span>&#160;    vec1 = tmp.row (0).cross (tmp.row (1));</div>
<div class="line"><a name="l00444"></a><span class="lineno">  444</span>&#160;    vec2 = tmp.row (0).cross (tmp.row (2));</div>
<div class="line"><a name="l00445"></a><span class="lineno">  445</span>&#160;    vec3 = tmp.row (1).cross (tmp.row (2));</div>
<div class="line"><a name="l00446"></a><span class="lineno">  446</span>&#160; </div>
<div class="line"><a name="l00447"></a><span class="lineno">  447</span>&#160;    len1 = vec1.squaredNorm ();</div>
<div class="line"><a name="l00448"></a><span class="lineno">  448</span>&#160;    len2 = vec2.squaredNorm ();</div>
<div class="line"><a name="l00449"></a><span class="lineno">  449</span>&#160;    len3 = vec3.squaredNorm ();</div>
<div class="line"><a name="l00450"></a><span class="lineno">  450</span>&#160;    <span class="keywordflow">if</span> (len1 &gt;= len2 &amp;&amp; len1 &gt;= len3)</div>
<div class="line"><a name="l00451"></a><span class="lineno">  451</span>&#160;    {</div>
<div class="line"><a name="l00452"></a><span class="lineno">  452</span>&#160;      mmax[0] = len1;</div>
<div class="line"><a name="l00453"></a><span class="lineno">  453</span>&#160;      evecs.col (0) = vec1 / std::sqrt (len1);</div>
<div class="line"><a name="l00454"></a><span class="lineno">  454</span>&#160;      min_el = len3 &lt;= mmax[min_el] ? 0 : min_el;</div>
<div class="line"><a name="l00455"></a><span class="lineno">  455</span>&#160;      max_el = len3 &gt; mmax[max_el] ? 0 : max_el;</div>
<div class="line"><a name="l00456"></a><span class="lineno">  456</span>&#160;    }</div>
<div class="line"><a name="l00457"></a><span class="lineno">  457</span>&#160;    <span class="keywordflow">else</span> <span class="keywordflow">if</span> (len2 &gt;= len1 &amp;&amp; len2 &gt;= len3)</div>
<div class="line"><a name="l00458"></a><span class="lineno">  458</span>&#160;    {</div>
<div class="line"><a name="l00459"></a><span class="lineno">  459</span>&#160;      mmax[0] = len2;</div>
<div class="line"><a name="l00460"></a><span class="lineno">  460</span>&#160;      evecs.col (0) = vec2 / std::sqrt (len2);</div>
<div class="line"><a name="l00461"></a><span class="lineno">  461</span>&#160;      min_el = len3 &lt;= mmax[min_el] ? 0 : min_el;</div>
<div class="line"><a name="l00462"></a><span class="lineno">  462</span>&#160;      max_el = len3 &gt; mmax[max_el] ? 0 : max_el;</div>
<div class="line"><a name="l00463"></a><span class="lineno">  463</span>&#160;    }</div>
<div class="line"><a name="l00464"></a><span class="lineno">  464</span>&#160;    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00465"></a><span class="lineno">  465</span>&#160;    {</div>
<div class="line"><a name="l00466"></a><span class="lineno">  466</span>&#160;      mmax[0] = len3;</div>
<div class="line"><a name="l00467"></a><span class="lineno">  467</span>&#160;      evecs.col (0) = vec3 / std::sqrt (len3);</div>
<div class="line"><a name="l00468"></a><span class="lineno">  468</span>&#160;      min_el = len3 &lt;= mmax[min_el] ? 0 : min_el;</div>
<div class="line"><a name="l00469"></a><span class="lineno">  469</span>&#160;      max_el = len3 &gt; mmax[max_el] ? 0 : max_el;</div>
<div class="line"><a name="l00470"></a><span class="lineno">  470</span>&#160;    }</div>
<div class="line"><a name="l00471"></a><span class="lineno">  471</span>&#160; </div>
<div class="line"><a name="l00472"></a><span class="lineno">  472</span>&#160;    <span class="keywordtype">unsigned</span> mid_el = 3 - min_el - max_el;</div>
<div class="line"><a name="l00473"></a><span class="lineno">  473</span>&#160;    evecs.col (min_el) = evecs.col ( (min_el + 1) % 3).cross (evecs.col ( (min_el + 2) % 3)).normalized ();</div>
<div class="line"><a name="l00474"></a><span class="lineno">  474</span>&#160;    evecs.col (mid_el) = evecs.col ( (mid_el + 1) % 3).cross (evecs.col ( (mid_el + 2) % 3)).normalized ();</div>
<div class="line"><a name="l00475"></a><span class="lineno">  475</span>&#160;<span class="preprocessor">#ifdef _WIN32</span></div>
<div class="line"><a name="l00476"></a><span class="lineno">  476</span>&#160;    <span class="keyword">delete</span> [] mmax;</div>
<div class="line"><a name="l00477"></a><span class="lineno">  477</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00478"></a><span class="lineno">  478</span>&#160;  }</div>
<div class="line"><a name="l00479"></a><span class="lineno">  479</span>&#160;  <span class="comment">// Rescale back to the original size.</span></div>
<div class="line"><a name="l00480"></a><span class="lineno">  480</span>&#160;  evals *= scale;</div>
<div class="line"><a name="l00481"></a><span class="lineno">  481</span>&#160;}</div>
<div class="line"><a name="l00482"></a><span class="lineno">  482</span>&#160; </div>
<div class="line"><a name="l00484"></a><span class="lineno">  484</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix&gt; <span class="keyword">inline</span> <span class="keyword">typename</span> Matrix::Scalar</div>
<div class="line"><a name="l00485"></a><span class="lineno"><a class="line" href="group__common.html#gad09b0c9a50601f3ae20a7babfd9a8d2d">  485</a></span>&#160;<a class="code" href="group__common.html#gad09b0c9a50601f3ae20a7babfd9a8d2d">pcl::invert2x2</a> (<span class="keyword">const</span> Matrix&amp; matrix, Matrix&amp; inverse)</div>
<div class="line"><a name="l00486"></a><span class="lineno">  486</span>&#160;{</div>
<div class="line"><a name="l00487"></a><span class="lineno">  487</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix::Scalar Scalar;</div>
<div class="line"><a name="l00488"></a><span class="lineno">  488</span>&#160;  Scalar det = matrix.coeff (0) * matrix.coeff (3) - matrix.coeff (1) * matrix.coeff (2);</div>
<div class="line"><a name="l00489"></a><span class="lineno">  489</span>&#160; </div>
<div class="line"><a name="l00490"></a><span class="lineno">  490</span>&#160;  <span class="keywordflow">if</span> (det != 0)</div>
<div class="line"><a name="l00491"></a><span class="lineno">  491</span>&#160;  {</div>
<div class="line"><a name="l00492"></a><span class="lineno">  492</span>&#160;    <span class="comment">//Scalar inv_det = Scalar (1.0) / det;</span></div>
<div class="line"><a name="l00493"></a><span class="lineno">  493</span>&#160;    inverse.coeffRef (0) = matrix.coeff (3);</div>
<div class="line"><a name="l00494"></a><span class="lineno">  494</span>&#160;    inverse.coeffRef (1) = -matrix.coeff (1);</div>
<div class="line"><a name="l00495"></a><span class="lineno">  495</span>&#160;    inverse.coeffRef (2) = -matrix.coeff (2);</div>
<div class="line"><a name="l00496"></a><span class="lineno">  496</span>&#160;    inverse.coeffRef (3) = matrix.coeff (0);</div>
<div class="line"><a name="l00497"></a><span class="lineno">  497</span>&#160;    inverse /= det;</div>
<div class="line"><a name="l00498"></a><span class="lineno">  498</span>&#160;  }</div>
<div class="line"><a name="l00499"></a><span class="lineno">  499</span>&#160;  <span class="keywordflow">return</span> det;</div>
<div class="line"><a name="l00500"></a><span class="lineno">  500</span>&#160;}</div>
<div class="line"><a name="l00501"></a><span class="lineno">  501</span>&#160; </div>
<div class="line"><a name="l00503"></a><span class="lineno">  503</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix&gt; <span class="keyword">inline</span> <span class="keyword">typename</span> Matrix::Scalar</div>
<div class="line"><a name="l00504"></a><span class="lineno"><a class="line" href="group__common.html#ga503f55a565c260660c6ac0461f17fa8f">  504</a></span>&#160;<a class="code" href="group__common.html#ga503f55a565c260660c6ac0461f17fa8f">pcl::invert3x3SymMatrix</a> (<span class="keyword">const</span> Matrix&amp; matrix, Matrix&amp; inverse)</div>
<div class="line"><a name="l00505"></a><span class="lineno">  505</span>&#160;{</div>
<div class="line"><a name="l00506"></a><span class="lineno">  506</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix::Scalar Scalar;</div>
<div class="line"><a name="l00507"></a><span class="lineno">  507</span>&#160;  <span class="comment">// elements</span></div>
<div class="line"><a name="l00508"></a><span class="lineno">  508</span>&#160;  <span class="comment">// a b c</span></div>
<div class="line"><a name="l00509"></a><span class="lineno">  509</span>&#160;  <span class="comment">// b d e</span></div>
<div class="line"><a name="l00510"></a><span class="lineno">  510</span>&#160;  <span class="comment">// c e f</span></div>
<div class="line"><a name="l00511"></a><span class="lineno">  511</span>&#160;  <span class="comment">//| a b c |-1             |   fd-ee    ce-bf   be-cd  |</span></div>
<div class="line"><a name="l00512"></a><span class="lineno">  512</span>&#160;  <span class="comment">//| b d e |    =  1/det * |   ce-bf    af-cc   bc-ae  |</span></div>
<div class="line"><a name="l00513"></a><span class="lineno">  513</span>&#160;  <span class="comment">//| c e f |               |   be-cd    bc-ae   ad-bb  |</span></div>
<div class="line"><a name="l00514"></a><span class="lineno">  514</span>&#160; </div>
<div class="line"><a name="l00515"></a><span class="lineno">  515</span>&#160;  <span class="comment">//det = a(fd-ee) + b(ec-fb) + c(eb-dc)</span></div>
<div class="line"><a name="l00516"></a><span class="lineno">  516</span>&#160; </div>
<div class="line"><a name="l00517"></a><span class="lineno">  517</span>&#160;  Scalar fd_ee = matrix.coeff (4) * matrix.coeff (8) - matrix.coeff (7) * matrix.coeff (5);</div>
<div class="line"><a name="l00518"></a><span class="lineno">  518</span>&#160;  Scalar ce_bf = matrix.coeff (2) * matrix.coeff (5) - matrix.coeff (1) * matrix.coeff (8);</div>
<div class="line"><a name="l00519"></a><span class="lineno">  519</span>&#160;  Scalar be_cd = matrix.coeff (1) * matrix.coeff (5) - matrix.coeff (2) * matrix.coeff (4);</div>
<div class="line"><a name="l00520"></a><span class="lineno">  520</span>&#160; </div>
<div class="line"><a name="l00521"></a><span class="lineno">  521</span>&#160;  Scalar det = matrix.coeff (0) * fd_ee + matrix.coeff (1) * ce_bf + matrix.coeff (2) * be_cd;</div>
<div class="line"><a name="l00522"></a><span class="lineno">  522</span>&#160; </div>
<div class="line"><a name="l00523"></a><span class="lineno">  523</span>&#160;  <span class="keywordflow">if</span> (det != 0)</div>
<div class="line"><a name="l00524"></a><span class="lineno">  524</span>&#160;  {</div>
<div class="line"><a name="l00525"></a><span class="lineno">  525</span>&#160;    <span class="comment">//Scalar inv_det = Scalar (1.0) / det;</span></div>
<div class="line"><a name="l00526"></a><span class="lineno">  526</span>&#160;    inverse.coeffRef (0) = fd_ee;</div>
<div class="line"><a name="l00527"></a><span class="lineno">  527</span>&#160;    inverse.coeffRef (1) = inverse.coeffRef (3) = ce_bf;</div>
<div class="line"><a name="l00528"></a><span class="lineno">  528</span>&#160;    inverse.coeffRef (2) = inverse.coeffRef (6) = be_cd;</div>
<div class="line"><a name="l00529"></a><span class="lineno">  529</span>&#160;    inverse.coeffRef (4) = (matrix.coeff (0) * matrix.coeff (8) - matrix.coeff (2) * matrix.coeff (2));</div>
<div class="line"><a name="l00530"></a><span class="lineno">  530</span>&#160;    inverse.coeffRef (5) = inverse.coeffRef (7) = (matrix.coeff (1) * matrix.coeff (2) - matrix.coeff (0) * matrix.coeff (5));</div>
<div class="line"><a name="l00531"></a><span class="lineno">  531</span>&#160;    inverse.coeffRef (8) = (matrix.coeff (0) * matrix.coeff (4) - matrix.coeff (1) * matrix.coeff (1));</div>
<div class="line"><a name="l00532"></a><span class="lineno">  532</span>&#160;    inverse /= det;</div>
<div class="line"><a name="l00533"></a><span class="lineno">  533</span>&#160;  }</div>
<div class="line"><a name="l00534"></a><span class="lineno">  534</span>&#160;  <span class="keywordflow">return</span> det;</div>
<div class="line"><a name="l00535"></a><span class="lineno">  535</span>&#160;}</div>
<div class="line"><a name="l00536"></a><span class="lineno">  536</span>&#160; </div>
<div class="line"><a name="l00538"></a><span class="lineno">  538</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix&gt; <span class="keyword">inline</span> <span class="keyword">typename</span> Matrix::Scalar</div>
<div class="line"><a name="l00539"></a><span class="lineno"><a class="line" href="group__common.html#gabb12d1f85437aafb0a3ac12af5633400">  539</a></span>&#160;<a class="code" href="group__common.html#gabb12d1f85437aafb0a3ac12af5633400">pcl::invert3x3Matrix</a> (<span class="keyword">const</span> Matrix&amp; matrix, Matrix&amp; inverse)</div>
<div class="line"><a name="l00540"></a><span class="lineno">  540</span>&#160;{</div>
<div class="line"><a name="l00541"></a><span class="lineno">  541</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Matrix::Scalar Scalar;</div>
<div class="line"><a name="l00542"></a><span class="lineno">  542</span>&#160; </div>
<div class="line"><a name="l00543"></a><span class="lineno">  543</span>&#160;  <span class="comment">//| a b c |-1             |   ie-hf    hc-ib   fb-ec  |</span></div>
<div class="line"><a name="l00544"></a><span class="lineno">  544</span>&#160;  <span class="comment">//| d e f |    =  1/det * |   gf-id    ia-gc   dc-fa  |</span></div>
<div class="line"><a name="l00545"></a><span class="lineno">  545</span>&#160;  <span class="comment">//| g h i |               |   hd-ge    gb-ha   ea-db  |</span></div>
<div class="line"><a name="l00546"></a><span class="lineno">  546</span>&#160;  <span class="comment">//det = a(ie-hf) + d(hc-ib) + g(fb-ec)</span></div>
<div class="line"><a name="l00547"></a><span class="lineno">  547</span>&#160; </div>
<div class="line"><a name="l00548"></a><span class="lineno">  548</span>&#160;  Scalar ie_hf = matrix.coeff (8) * matrix.coeff (4) - matrix.coeff (7) * matrix.coeff (5);</div>
<div class="line"><a name="l00549"></a><span class="lineno">  549</span>&#160;  Scalar hc_ib = matrix.coeff (7) * matrix.coeff (2) - matrix.coeff (8) * matrix.coeff (1);</div>
<div class="line"><a name="l00550"></a><span class="lineno">  550</span>&#160;  Scalar fb_ec = matrix.coeff (5) * matrix.coeff (1) - matrix.coeff (4) * matrix.coeff (2);</div>
<div class="line"><a name="l00551"></a><span class="lineno">  551</span>&#160;  Scalar det = matrix.coeff (0) * (ie_hf) + matrix.coeff (3) * (hc_ib) + matrix.coeff (6) * (fb_ec);</div>
<div class="line"><a name="l00552"></a><span class="lineno">  552</span>&#160; </div>
<div class="line"><a name="l00553"></a><span class="lineno">  553</span>&#160;  <span class="keywordflow">if</span> (det != 0)</div>
<div class="line"><a name="l00554"></a><span class="lineno">  554</span>&#160;  {</div>
<div class="line"><a name="l00555"></a><span class="lineno">  555</span>&#160;    inverse.coeffRef (0) = ie_hf;</div>
<div class="line"><a name="l00556"></a><span class="lineno">  556</span>&#160;    inverse.coeffRef (1) = hc_ib;</div>
<div class="line"><a name="l00557"></a><span class="lineno">  557</span>&#160;    inverse.coeffRef (2) = fb_ec;</div>
<div class="line"><a name="l00558"></a><span class="lineno">  558</span>&#160;    inverse.coeffRef (3) = matrix.coeff (6) * matrix.coeff (5) - matrix.coeff (8) * matrix.coeff (3);</div>
<div class="line"><a name="l00559"></a><span class="lineno">  559</span>&#160;    inverse.coeffRef (4) = matrix.coeff (8) * matrix.coeff (0) - matrix.coeff (6) * matrix.coeff (2);</div>
<div class="line"><a name="l00560"></a><span class="lineno">  560</span>&#160;    inverse.coeffRef (5) = matrix.coeff (3) * matrix.coeff (2) - matrix.coeff (5) * matrix.coeff (0);</div>
<div class="line"><a name="l00561"></a><span class="lineno">  561</span>&#160;    inverse.coeffRef (6) = matrix.coeff (7) * matrix.coeff (3) - matrix.coeff (6) * matrix.coeff (4);</div>
<div class="line"><a name="l00562"></a><span class="lineno">  562</span>&#160;    inverse.coeffRef (7) = matrix.coeff (6) * matrix.coeff (1) - matrix.coeff (7) * matrix.coeff (0);</div>
<div class="line"><a name="l00563"></a><span class="lineno">  563</span>&#160;    inverse.coeffRef (8) = matrix.coeff (4) * matrix.coeff (0) - matrix.coeff (3) * matrix.coeff (1);</div>
<div class="line"><a name="l00564"></a><span class="lineno">  564</span>&#160; </div>
<div class="line"><a name="l00565"></a><span class="lineno">  565</span>&#160;    inverse /= det;</div>
<div class="line"><a name="l00566"></a><span class="lineno">  566</span>&#160;  }</div>
<div class="line"><a name="l00567"></a><span class="lineno">  567</span>&#160;  <span class="keywordflow">return</span> det;</div>
<div class="line"><a name="l00568"></a><span class="lineno">  568</span>&#160;}</div>
<div class="line"><a name="l00569"></a><span class="lineno">  569</span>&#160; </div>
<div class="line"><a name="l00571"></a><span class="lineno">  571</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Matrix&gt; <span class="keyword">inline</span> <span class="keyword">typename</span> Matrix::Scalar</div>
<div class="line"><a name="l00572"></a><span class="lineno"><a class="line" href="group__common.html#ga44d0048ba1efd11359011eb47f6c92fa">  572</a></span>&#160;<a class="code" href="group__common.html#ga44d0048ba1efd11359011eb47f6c92fa">pcl::determinant3x3Matrix</a> (<span class="keyword">const</span> Matrix&amp; matrix)</div>
<div class="line"><a name="l00573"></a><span class="lineno">  573</span>&#160;{</div>
<div class="line"><a name="l00574"></a><span class="lineno">  574</span>&#160;  <span class="comment">// result is independent of Row/Col Major storage!</span></div>
<div class="line"><a name="l00575"></a><span class="lineno">  575</span>&#160;  <span class="keywordflow">return</span> matrix.coeff (0) * (matrix.coeff (4) * matrix.coeff (8) - matrix.coeff (5) * matrix.coeff (7)) +</div>
<div class="line"><a name="l00576"></a><span class="lineno">  576</span>&#160;         matrix.coeff (1) * (matrix.coeff (5) * matrix.coeff (6) - matrix.coeff (3) * matrix.coeff (8)) +</div>
<div class="line"><a name="l00577"></a><span class="lineno">  577</span>&#160;         matrix.coeff (2) * (matrix.coeff (3) * matrix.coeff (7) - matrix.coeff (4) * matrix.coeff (6)) ;</div>
<div class="line"><a name="l00578"></a><span class="lineno">  578</span>&#160;}</div>
<div class="line"><a name="l00579"></a><span class="lineno">  579</span>&#160; </div>
<div class="line"><a name="l00581"></a><span class="lineno">  581</span>&#160;<span class="keywordtype">void</span> </div>
<div class="line"><a name="l00582"></a><span class="lineno"><a class="line" href="group__common.html#gaf457d33994792e63129de9709dcdf329">  582</a></span>&#160;<a class="code" href="group__common.html#gaf457d33994792e63129de9709dcdf329">pcl::getTransFromUnitVectorsZY</a> (<span class="keyword">const</span> Eigen::Vector3f&amp; z_axis, </div>
<div class="line"><a name="l00583"></a><span class="lineno">  583</span>&#160;                                <span class="keyword">const</span> Eigen::Vector3f&amp; y_direction, </div>
<div class="line"><a name="l00584"></a><span class="lineno">  584</span>&#160;                                Eigen::Affine3f&amp; transformation)</div>
<div class="line"><a name="l00585"></a><span class="lineno">  585</span>&#160;{</div>
<div class="line"><a name="l00586"></a><span class="lineno">  586</span>&#160;  Eigen::Vector3f tmp0 = (y_direction.cross(z_axis)).normalized();</div>
<div class="line"><a name="l00587"></a><span class="lineno">  587</span>&#160;  Eigen::Vector3f tmp1 = (z_axis.cross(tmp0)).normalized();</div>
<div class="line"><a name="l00588"></a><span class="lineno">  588</span>&#160;  Eigen::Vector3f tmp2 = z_axis.normalized();</div>
<div class="line"><a name="l00589"></a><span class="lineno">  589</span>&#160;  </div>
<div class="line"><a name="l00590"></a><span class="lineno">  590</span>&#160;  transformation(0,0)=tmp0[0]; transformation(0,1)=tmp0[1]; transformation(0,2)=tmp0[2]; transformation(0,3)=0.0f;</div>
<div class="line"><a name="l00591"></a><span class="lineno">  591</span>&#160;  transformation(1,0)=tmp1[0]; transformation(1,1)=tmp1[1]; transformation(1,2)=tmp1[2]; transformation(1,3)=0.0f;</div>
<div class="line"><a name="l00592"></a><span class="lineno">  592</span>&#160;  transformation(2,0)=tmp2[0]; transformation(2,1)=tmp2[1]; transformation(2,2)=tmp2[2]; transformation(2,3)=0.0f;</div>
<div class="line"><a name="l00593"></a><span class="lineno">  593</span>&#160;  transformation(3,0)=0.0f;    transformation(3,1)=0.0f;    transformation(3,2)=0.0f;    transformation(3,3)=1.0f;</div>
<div class="line"><a name="l00594"></a><span class="lineno">  594</span>&#160;}</div>
<div class="line"><a name="l00595"></a><span class="lineno">  595</span>&#160; </div>
<div class="line"><a name="l00597"></a><span class="lineno">  597</span>&#160;Eigen::Affine3f </div>
<div class="line"><a name="l00598"></a><span class="lineno"><a class="line" href="group__common.html#ga58d47eda3c3f5f91125296fd7d202ebb">  598</a></span>&#160;<a class="code" href="group__common.html#gaf457d33994792e63129de9709dcdf329">pcl::getTransFromUnitVectorsZY</a> (<span class="keyword">const</span> Eigen::Vector3f&amp; z_axis, </div>
<div class="line"><a name="l00599"></a><span class="lineno">  599</span>&#160;                                <span class="keyword">const</span> Eigen::Vector3f&amp; y_direction)</div>
<div class="line"><a name="l00600"></a><span class="lineno">  600</span>&#160;{</div>
<div class="line"><a name="l00601"></a><span class="lineno">  601</span>&#160;  Eigen::Affine3f transformation;</div>
<div class="line"><a name="l00602"></a><span class="lineno">  602</span>&#160;  <a class="code" href="group__common.html#gaf457d33994792e63129de9709dcdf329">getTransFromUnitVectorsZY</a> (z_axis, y_direction, transformation);</div>
<div class="line"><a name="l00603"></a><span class="lineno">  603</span>&#160;  <span class="keywordflow">return</span> (transformation);</div>
<div class="line"><a name="l00604"></a><span class="lineno">  604</span>&#160;}</div>
<div class="line"><a name="l00605"></a><span class="lineno">  605</span>&#160; </div>
<div class="line"><a name="l00607"></a><span class="lineno">  607</span>&#160;<span class="keywordtype">void</span> </div>
<div class="line"><a name="l00608"></a><span class="lineno"><a class="line" href="group__common.html#ga8319aa7921bdc742a9d0f95458e9cfe0">  608</a></span>&#160;<a class="code" href="group__common.html#ga8319aa7921bdc742a9d0f95458e9cfe0">pcl::getTransFromUnitVectorsXY</a> (<span class="keyword">const</span> Eigen::Vector3f&amp; x_axis, </div>
<div class="line"><a name="l00609"></a><span class="lineno">  609</span>&#160;                                <span class="keyword">const</span> Eigen::Vector3f&amp; y_direction, </div>
<div class="line"><a name="l00610"></a><span class="lineno">  610</span>&#160;                                Eigen::Affine3f&amp; transformation)</div>
<div class="line"><a name="l00611"></a><span class="lineno">  611</span>&#160;{</div>
<div class="line"><a name="l00612"></a><span class="lineno">  612</span>&#160;  Eigen::Vector3f tmp2 = (x_axis.cross(y_direction)).normalized();</div>
<div class="line"><a name="l00613"></a><span class="lineno">  613</span>&#160;  Eigen::Vector3f tmp1 = (tmp2.cross(x_axis)).normalized();</div>
<div class="line"><a name="l00614"></a><span class="lineno">  614</span>&#160;  Eigen::Vector3f tmp0 = x_axis.normalized();</div>
<div class="line"><a name="l00615"></a><span class="lineno">  615</span>&#160;  </div>
<div class="line"><a name="l00616"></a><span class="lineno">  616</span>&#160;  transformation(0,0)=tmp0[0]; transformation(0,1)=tmp0[1]; transformation(0,2)=tmp0[2]; transformation(0,3)=0.0f;</div>
<div class="line"><a name="l00617"></a><span class="lineno">  617</span>&#160;  transformation(1,0)=tmp1[0]; transformation(1,1)=tmp1[1]; transformation(1,2)=tmp1[2]; transformation(1,3)=0.0f;</div>
<div class="line"><a name="l00618"></a><span class="lineno">  618</span>&#160;  transformation(2,0)=tmp2[0]; transformation(2,1)=tmp2[1]; transformation(2,2)=tmp2[2]; transformation(2,3)=0.0f;</div>
<div class="line"><a name="l00619"></a><span class="lineno">  619</span>&#160;  transformation(3,0)=0.0f;    transformation(3,1)=0.0f;    transformation(3,2)=0.0f;    transformation(3,3)=1.0f;</div>
<div class="line"><a name="l00620"></a><span class="lineno">  620</span>&#160;}</div>
<div class="line"><a name="l00621"></a><span class="lineno">  621</span>&#160; </div>
<div class="line"><a name="l00623"></a><span class="lineno">  623</span>&#160;Eigen::Affine3f </div>
<div class="line"><a name="l00624"></a><span class="lineno"><a class="line" href="group__common.html#ga8933c653f39db3636bfbdd262278edcb">  624</a></span>&#160;<a class="code" href="group__common.html#ga8319aa7921bdc742a9d0f95458e9cfe0">pcl::getTransFromUnitVectorsXY</a> (<span class="keyword">const</span> Eigen::Vector3f&amp; x_axis, </div>
<div class="line"><a name="l00625"></a><span class="lineno">  625</span>&#160;                                <span class="keyword">const</span> Eigen::Vector3f&amp; y_direction)</div>
<div class="line"><a name="l00626"></a><span class="lineno">  626</span>&#160;{</div>
<div class="line"><a name="l00627"></a><span class="lineno">  627</span>&#160;  Eigen::Affine3f transformation;</div>
<div class="line"><a name="l00628"></a><span class="lineno">  628</span>&#160;  <a class="code" href="group__common.html#ga8319aa7921bdc742a9d0f95458e9cfe0">getTransFromUnitVectorsXY</a> (x_axis, y_direction, transformation);</div>
<div class="line"><a name="l00629"></a><span class="lineno">  629</span>&#160;  <span class="keywordflow">return</span> (transformation);</div>
<div class="line"><a name="l00630"></a><span class="lineno">  630</span>&#160;}</div>
<div class="line"><a name="l00631"></a><span class="lineno">  631</span>&#160; </div>
<div class="line"><a name="l00633"></a><span class="lineno">  633</span>&#160;<span class="keywordtype">void</span> </div>
<div class="line"><a name="l00634"></a><span class="lineno"><a class="line" href="group__common.html#ga7d1f523f342ff69277f23ea9f02fc5a6">  634</a></span>&#160;<a class="code" href="group__common.html#ga7d1f523f342ff69277f23ea9f02fc5a6">pcl::getTransformationFromTwoUnitVectors</a> (<span class="keyword">const</span> Eigen::Vector3f&amp; y_direction, </div>
<div class="line"><a name="l00635"></a><span class="lineno">  635</span>&#160;                                          <span class="keyword">const</span> Eigen::Vector3f&amp; z_axis, </div>
<div class="line"><a name="l00636"></a><span class="lineno">  636</span>&#160;                                          Eigen::Affine3f&amp; transformation)</div>
<div class="line"><a name="l00637"></a><span class="lineno">  637</span>&#160;{</div>
<div class="line"><a name="l00638"></a><span class="lineno">  638</span>&#160;  <a class="code" href="group__common.html#gaf457d33994792e63129de9709dcdf329">getTransFromUnitVectorsZY</a> (z_axis, y_direction, transformation);</div>
<div class="line"><a name="l00639"></a><span class="lineno">  639</span>&#160;}</div>
<div class="line"><a name="l00640"></a><span class="lineno">  640</span>&#160; </div>
<div class="line"><a name="l00642"></a><span class="lineno">  642</span>&#160;Eigen::Affine3f </div>
<div class="line"><a name="l00643"></a><span class="lineno"><a class="line" href="group__common.html#gada89edf1699e05ecf7355738e9f56f6b">  643</a></span>&#160;<a class="code" href="group__common.html#ga7d1f523f342ff69277f23ea9f02fc5a6">pcl::getTransformationFromTwoUnitVectors</a> (<span class="keyword">const</span> Eigen::Vector3f&amp; y_direction, </div>
<div class="line"><a name="l00644"></a><span class="lineno">  644</span>&#160;                                          <span class="keyword">const</span> Eigen::Vector3f&amp; z_axis)</div>
<div class="line"><a name="l00645"></a><span class="lineno">  645</span>&#160;{</div>
<div class="line"><a name="l00646"></a><span class="lineno">  646</span>&#160;  Eigen::Affine3f transformation;</div>
<div class="line"><a name="l00647"></a><span class="lineno">  647</span>&#160;  <a class="code" href="group__common.html#ga7d1f523f342ff69277f23ea9f02fc5a6">getTransformationFromTwoUnitVectors</a> (y_direction, z_axis, transformation);</div>
<div class="line"><a name="l00648"></a><span class="lineno">  648</span>&#160;  <span class="keywordflow">return</span> (transformation);</div>
<div class="line"><a name="l00649"></a><span class="lineno">  649</span>&#160;}</div>
<div class="line"><a name="l00650"></a><span class="lineno">  650</span>&#160; </div>
<div class="line"><a name="l00651"></a><span class="lineno">  651</span>&#160;<span class="keywordtype">void</span> </div>
<div class="line"><a name="l00652"></a><span class="lineno"><a class="line" href="group__common.html#ga4375e99ec2ae368eec9379f506568611">  652</a></span>&#160;<a class="code" href="group__common.html#ga4375e99ec2ae368eec9379f506568611">pcl::getTransformationFromTwoUnitVectorsAndOrigin</a> (<span class="keyword">const</span> Eigen::Vector3f&amp; y_direction, </div>
<div class="line"><a name="l00653"></a><span class="lineno">  653</span>&#160;                                                   <span class="keyword">const</span> Eigen::Vector3f&amp; z_axis,</div>
<div class="line"><a name="l00654"></a><span class="lineno">  654</span>&#160;                                                   <span class="keyword">const</span> Eigen::Vector3f&amp; origin, </div>
<div class="line"><a name="l00655"></a><span class="lineno">  655</span>&#160;                                                   Eigen::Affine3f&amp; transformation)</div>
<div class="line"><a name="l00656"></a><span class="lineno">  656</span>&#160;{</div>
<div class="line"><a name="l00657"></a><span class="lineno">  657</span>&#160;  <a class="code" href="group__common.html#ga7d1f523f342ff69277f23ea9f02fc5a6">getTransformationFromTwoUnitVectors</a>(y_direction, z_axis, transformation);</div>
<div class="line"><a name="l00658"></a><span class="lineno">  658</span>&#160;  Eigen::Vector3f translation = transformation*origin;</div>
<div class="line"><a name="l00659"></a><span class="lineno">  659</span>&#160;  transformation(0,3)=-translation[0];  transformation(1,3)=-translation[1];  transformation(2,3)=-translation[2];</div>
<div class="line"><a name="l00660"></a><span class="lineno">  660</span>&#160;}</div>
<div class="line"><a name="l00661"></a><span class="lineno">  661</span>&#160; </div>
<div class="line"><a name="l00663"></a><span class="lineno">  663</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00664"></a><span class="lineno"><a class="line" href="group__common.html#ga637da495fec59c1c1d186aa6e3bac15b">  664</a></span>&#160;<a class="code" href="group__common.html#ga637da495fec59c1c1d186aa6e3bac15b">pcl::getEulerAngles</a> (<span class="keyword">const</span> Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt; &amp;t, Scalar &amp;roll, Scalar &amp;pitch, Scalar &amp;yaw)</div>
<div class="line"><a name="l00665"></a><span class="lineno">  665</span>&#160;{</div>
<div class="line"><a name="l00666"></a><span class="lineno">  666</span>&#160;  roll = atan2 (t (2, 1), t (2, 2));</div>
<div class="line"><a name="l00667"></a><span class="lineno">  667</span>&#160;  pitch = asin (-t (2, 0));</div>
<div class="line"><a name="l00668"></a><span class="lineno">  668</span>&#160;  yaw = atan2 (t (1, 0), t (0, 0));</div>
<div class="line"><a name="l00669"></a><span class="lineno">  669</span>&#160;}</div>
<div class="line"><a name="l00670"></a><span class="lineno">  670</span>&#160; </div>
<div class="line"><a name="l00672"></a><span class="lineno">  672</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00673"></a><span class="lineno"><a class="line" href="group__common.html#ga3e52d439a979e71096f4dd50f1298f32">  673</a></span>&#160;<a class="code" href="group__common.html#ga3e52d439a979e71096f4dd50f1298f32">pcl::getTranslationAndEulerAngles</a> (<span class="keyword">const</span> Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt; &amp;t,</div>
<div class="line"><a name="l00674"></a><span class="lineno">  674</span>&#160;                                  Scalar &amp;x, Scalar &amp;y, Scalar &amp;z,</div>
<div class="line"><a name="l00675"></a><span class="lineno">  675</span>&#160;                                  Scalar &amp;roll, Scalar &amp;pitch, Scalar &amp;yaw)</div>
<div class="line"><a name="l00676"></a><span class="lineno">  676</span>&#160;{</div>
<div class="line"><a name="l00677"></a><span class="lineno">  677</span>&#160;  x = t (0, 3);</div>
<div class="line"><a name="l00678"></a><span class="lineno">  678</span>&#160;  y = t (1, 3);</div>
<div class="line"><a name="l00679"></a><span class="lineno">  679</span>&#160;  z = t (2, 3);</div>
<div class="line"><a name="l00680"></a><span class="lineno">  680</span>&#160;  roll = atan2 (t (2, 1), t (2, 2));</div>
<div class="line"><a name="l00681"></a><span class="lineno">  681</span>&#160;  pitch = asin (-t (2, 0));</div>
<div class="line"><a name="l00682"></a><span class="lineno">  682</span>&#160;  yaw = atan2 (t (1, 0), t (0, 0));</div>
<div class="line"><a name="l00683"></a><span class="lineno">  683</span>&#160;}</div>
<div class="line"><a name="l00684"></a><span class="lineno">  684</span>&#160; </div>
<div class="line"><a name="l00686"></a><span class="lineno">  686</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt; <span class="keywordtype">void</span> </div>
<div class="line"><a name="l00687"></a><span class="lineno"><a class="line" href="group__common.html#ga5cc746d1fd72f99fee462ed1a9e4abea">  687</a></span>&#160;<a class="code" href="group__common.html#ga5cc746d1fd72f99fee462ed1a9e4abea">pcl::getTransformation</a> (Scalar x, Scalar y, Scalar z, </div>
<div class="line"><a name="l00688"></a><span class="lineno">  688</span>&#160;                        Scalar roll, Scalar pitch, Scalar yaw, </div>
<div class="line"><a name="l00689"></a><span class="lineno">  689</span>&#160;                        Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt; &amp;t)</div>
<div class="line"><a name="l00690"></a><span class="lineno">  690</span>&#160;{</div>
<div class="line"><a name="l00691"></a><span class="lineno">  691</span>&#160;  Scalar A = cos (yaw),  B = sin (yaw),  C  = cos (pitch), D  = sin (pitch),</div>
<div class="line"><a name="l00692"></a><span class="lineno">  692</span>&#160;         E = cos (roll), F = sin (roll), DE = D*E,         DF = D*F;</div>
<div class="line"><a name="l00693"></a><span class="lineno">  693</span>&#160; </div>
<div class="line"><a name="l00694"></a><span class="lineno">  694</span>&#160;  t (0, 0) = A*C;  t (0, 1) = A*DF - B*E;  t (0, 2) = B*F + A*DE;  t (0, 3) = x;</div>
<div class="line"><a name="l00695"></a><span class="lineno">  695</span>&#160;  t (1, 0) = B*C;  t (1, 1) = A*E + B*DF;  t (1, 2) = B*DE - A*F;  t (1, 3) = y;</div>
<div class="line"><a name="l00696"></a><span class="lineno">  696</span>&#160;  t (2, 0) = -D;   t (2, 1) = C*F;         t (2, 2) = C*E;         t (2, 3) = z;</div>
<div class="line"><a name="l00697"></a><span class="lineno">  697</span>&#160;  t (3, 0) = 0;    t (3, 1) = 0;           t (3, 2) = 0;           t (3, 3) = 1;</div>
<div class="line"><a name="l00698"></a><span class="lineno">  698</span>&#160;}</div>
<div class="line"><a name="l00699"></a><span class="lineno">  699</span>&#160; </div>
<div class="line"><a name="l00701"></a><span class="lineno">  701</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived&gt; <span class="keywordtype">void</span> </div>
<div class="line"><a name="l00702"></a><span class="lineno"><a class="line" href="group__common.html#gacc18ebcacd806fd0c9336fe2f8b7208c">  702</a></span>&#160;<a class="code" href="group__common.html#gacc18ebcacd806fd0c9336fe2f8b7208c">pcl::saveBinary</a> (<span class="keyword">const</span> Eigen::MatrixBase&lt;Derived&gt;&amp; matrix, std::ostream&amp; file)</div>
<div class="line"><a name="l00703"></a><span class="lineno">  703</span>&#160;{</div>
<div class="line"><a name="l00704"></a><span class="lineno">  704</span>&#160;  uint32_t rows = <span class="keyword">static_cast&lt;</span>uint32_t<span class="keyword">&gt;</span> (matrix.rows ()), cols = <span class="keyword">static_cast&lt;</span>uint32_t<span class="keyword">&gt;</span> (matrix.cols ());</div>
<div class="line"><a name="l00705"></a><span class="lineno">  705</span>&#160;  file.write (<span class="keyword">reinterpret_cast&lt;</span><span class="keywordtype">char</span>*<span class="keyword">&gt;</span> (&amp;rows), <span class="keyword">sizeof</span> (rows));</div>
<div class="line"><a name="l00706"></a><span class="lineno">  706</span>&#160;  file.write (<span class="keyword">reinterpret_cast&lt;</span><span class="keywordtype">char</span>*<span class="keyword">&gt;</span> (&amp;cols), <span class="keyword">sizeof</span> (cols));</div>
<div class="line"><a name="l00707"></a><span class="lineno">  707</span>&#160;  <span class="keywordflow">for</span> (uint32_t i = 0; i &lt; rows; ++i)</div>
<div class="line"><a name="l00708"></a><span class="lineno">  708</span>&#160;    <span class="keywordflow">for</span> (uint32_t j = 0; j &lt; cols; ++j)</div>
<div class="line"><a name="l00709"></a><span class="lineno">  709</span>&#160;    {</div>
<div class="line"><a name="l00710"></a><span class="lineno">  710</span>&#160;      <span class="keyword">typename</span> Derived::Scalar tmp = matrix(i,j);</div>
<div class="line"><a name="l00711"></a><span class="lineno">  711</span>&#160;      file.write (<span class="keyword">reinterpret_cast&lt;</span><span class="keyword">const </span><span class="keywordtype">char</span>*<span class="keyword">&gt;</span> (&amp;tmp), <span class="keyword">sizeof</span> (tmp));</div>
<div class="line"><a name="l00712"></a><span class="lineno">  712</span>&#160;    }</div>
<div class="line"><a name="l00713"></a><span class="lineno">  713</span>&#160;}</div>
<div class="line"><a name="l00714"></a><span class="lineno">  714</span>&#160; </div>
<div class="line"><a name="l00716"></a><span class="lineno">  716</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived&gt; <span class="keywordtype">void</span> </div>
<div class="line"><a name="l00717"></a><span class="lineno"><a class="line" href="group__common.html#ga5281205532955d384c8aa22ff4ff5e80">  717</a></span>&#160;<a class="code" href="group__common.html#ga5281205532955d384c8aa22ff4ff5e80">pcl::loadBinary</a> (Eigen::MatrixBase&lt;Derived&gt; <span class="keyword">const</span> &amp; matrix_, std::istream&amp; file)</div>
<div class="line"><a name="l00718"></a><span class="lineno">  718</span>&#160;{</div>
<div class="line"><a name="l00719"></a><span class="lineno">  719</span>&#160;  Eigen::MatrixBase&lt;Derived&gt; &amp;matrix = <span class="keyword">const_cast&lt;</span>Eigen::MatrixBase&lt;Derived&gt; &amp;<span class="keyword">&gt;</span> (matrix_);</div>
<div class="line"><a name="l00720"></a><span class="lineno">  720</span>&#160; </div>
<div class="line"><a name="l00721"></a><span class="lineno">  721</span>&#160;  uint32_t rows, cols;</div>
<div class="line"><a name="l00722"></a><span class="lineno">  722</span>&#160;  file.read (<span class="keyword">reinterpret_cast&lt;</span><span class="keywordtype">char</span>*<span class="keyword">&gt;</span> (&amp;rows), <span class="keyword">sizeof</span> (rows));</div>
<div class="line"><a name="l00723"></a><span class="lineno">  723</span>&#160;  file.read (<span class="keyword">reinterpret_cast&lt;</span><span class="keywordtype">char</span>*<span class="keyword">&gt;</span> (&amp;cols), <span class="keyword">sizeof</span> (cols));</div>
<div class="line"><a name="l00724"></a><span class="lineno">  724</span>&#160;  <span class="keywordflow">if</span> (matrix.rows () != <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(rows) || matrix.cols () != <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(cols))</div>
<div class="line"><a name="l00725"></a><span class="lineno">  725</span>&#160;    matrix.derived().resize(rows, cols);</div>
<div class="line"><a name="l00726"></a><span class="lineno">  726</span>&#160;  </div>
<div class="line"><a name="l00727"></a><span class="lineno">  727</span>&#160;  <span class="keywordflow">for</span> (uint32_t i = 0; i &lt; rows; ++i)</div>
<div class="line"><a name="l00728"></a><span class="lineno">  728</span>&#160;    <span class="keywordflow">for</span> (uint32_t j = 0; j &lt; cols; ++j)</div>
<div class="line"><a name="l00729"></a><span class="lineno">  729</span>&#160;    {</div>
<div class="line"><a name="l00730"></a><span class="lineno">  730</span>&#160;      <span class="keyword">typename</span> Derived::Scalar tmp;</div>
<div class="line"><a name="l00731"></a><span class="lineno">  731</span>&#160;      file.read (<span class="keyword">reinterpret_cast&lt;</span><span class="keywordtype">char</span>*<span class="keyword">&gt;</span> (&amp;tmp), <span class="keyword">sizeof</span> (tmp));</div>
<div class="line"><a name="l00732"></a><span class="lineno">  732</span>&#160;      matrix (i, j) = tmp;</div>
<div class="line"><a name="l00733"></a><span class="lineno">  733</span>&#160;    }</div>
<div class="line"><a name="l00734"></a><span class="lineno">  734</span>&#160;}</div>
<div class="line"><a name="l00735"></a><span class="lineno">  735</span>&#160; </div>
<div class="line"><a name="l00737"></a><span class="lineno">  737</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Derived, <span class="keyword">typename</span> OtherDerived&gt; </div>
<div class="line"><a name="l00738"></a><span class="lineno">  738</span>&#160;<span class="keyword">typename</span> Eigen::internal::umeyama_transform_matrix_type&lt;Derived, OtherDerived&gt;::type</div>
<div class="line"><a name="l00739"></a><span class="lineno">  739</span>&#160;pcl::umeyama (<span class="keyword">const</span> Eigen::MatrixBase&lt;Derived&gt;&amp; src, <span class="keyword">const</span> Eigen::MatrixBase&lt;OtherDerived&gt;&amp; dst, <span class="keywordtype">bool</span> with_scaling)</div>
<div class="line"><a name="l00740"></a><span class="lineno">  740</span>&#160;{</div>
<div class="line"><a name="l00741"></a><span class="lineno">  741</span>&#160;<span class="preprocessor">#if EIGEN_VERSION_AT_LEAST (3, 3, 0)</span></div>
<div class="line"><a name="l00742"></a><span class="lineno">  742</span>&#160;  <span class="keywordflow">return</span> Eigen::umeyama (src, dst, with_scaling);</div>
<div class="line"><a name="l00743"></a><span class="lineno">  743</span>&#160;<span class="preprocessor">#else</span></div>
<div class="line"><a name="l00744"></a><span class="lineno">  744</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Eigen::internal::umeyama_transform_matrix_type&lt;Derived, OtherDerived&gt;::type TransformationMatrixType;</div>
<div class="line"><a name="l00745"></a><span class="lineno">  745</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Eigen::internal::traits&lt;TransformationMatrixType&gt;::Scalar Scalar;</div>
<div class="line"><a name="l00746"></a><span class="lineno">  746</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Eigen::NumTraits&lt;Scalar&gt;::Real RealScalar;</div>
<div class="line"><a name="l00747"></a><span class="lineno">  747</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::Index Index;</div>
<div class="line"><a name="l00748"></a><span class="lineno">  748</span>&#160; </div>
<div class="line"><a name="l00749"></a><span class="lineno">  749</span>&#160;  EIGEN_STATIC_ASSERT (!Eigen::NumTraits&lt;Scalar&gt;::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)</div>
<div class="line"><a name="l00750"></a><span class="lineno">  750</span>&#160;  EIGEN_STATIC_ASSERT ((Eigen::internal::is_same&lt;Scalar, <span class="keyword">typename</span> Eigen::internal::traits&lt;OtherDerived&gt;::Scalar&gt;::value),</div>
<div class="line"><a name="l00751"></a><span class="lineno">  751</span>&#160;    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)</div>
<div class="line"><a name="l00752"></a><span class="lineno">  752</span>&#160; </div>
<div class="line"><a name="l00753"></a><span class="lineno">  753</span>&#160;  <span class="keyword">enum</span> { Dimension = PCL_EIGEN_SIZE_MIN_PREFER_DYNAMIC (Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };</div>
<div class="line"><a name="l00754"></a><span class="lineno">  754</span>&#160; </div>
<div class="line"><a name="l00755"></a><span class="lineno">  755</span>&#160;  <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar, Dimension, 1&gt; VectorType;</div>
<div class="line"><a name="l00756"></a><span class="lineno">  756</span>&#160;  <span class="keyword">typedef</span> Eigen::Matrix&lt;Scalar, Dimension, Dimension&gt; MatrixType;</div>
<div class="line"><a name="l00757"></a><span class="lineno">  757</span>&#160;  <span class="keyword">typedef</span> <span class="keyword">typename</span> Eigen::internal::plain_matrix_type_row_major&lt;Derived&gt;::type RowMajorMatrixType;</div>
<div class="line"><a name="l00758"></a><span class="lineno">  758</span>&#160; </div>
<div class="line"><a name="l00759"></a><span class="lineno">  759</span>&#160;  <span class="keyword">const</span> Index m = src.rows (); <span class="comment">// dimension</span></div>
<div class="line"><a name="l00760"></a><span class="lineno">  760</span>&#160;  <span class="keyword">const</span> Index n = src.cols (); <span class="comment">// number of measurements</span></div>
<div class="line"><a name="l00761"></a><span class="lineno">  761</span>&#160; </div>
<div class="line"><a name="l00762"></a><span class="lineno">  762</span>&#160;  <span class="comment">// required for demeaning ...</span></div>
<div class="line"><a name="l00763"></a><span class="lineno">  763</span>&#160;  <span class="keyword">const</span> RealScalar one_over_n = 1 / <span class="keyword">static_cast&lt;</span>RealScalar<span class="keyword">&gt;</span> (n);</div>
<div class="line"><a name="l00764"></a><span class="lineno">  764</span>&#160; </div>
<div class="line"><a name="l00765"></a><span class="lineno">  765</span>&#160;  <span class="comment">// computation of mean</span></div>
<div class="line"><a name="l00766"></a><span class="lineno">  766</span>&#160;  <span class="keyword">const</span> VectorType src_mean = src.rowwise ().sum () * one_over_n;</div>
<div class="line"><a name="l00767"></a><span class="lineno">  767</span>&#160;  <span class="keyword">const</span> VectorType dst_mean = dst.rowwise ().sum () * one_over_n;</div>
<div class="line"><a name="l00768"></a><span class="lineno">  768</span>&#160; </div>
<div class="line"><a name="l00769"></a><span class="lineno">  769</span>&#160;  <span class="comment">// demeaning of src and dst points</span></div>
<div class="line"><a name="l00770"></a><span class="lineno">  770</span>&#160;  <span class="keyword">const</span> RowMajorMatrixType src_demean = src.colwise () - src_mean;</div>
<div class="line"><a name="l00771"></a><span class="lineno">  771</span>&#160;  <span class="keyword">const</span> RowMajorMatrixType dst_demean = dst.colwise () - dst_mean;</div>
<div class="line"><a name="l00772"></a><span class="lineno">  772</span>&#160; </div>
<div class="line"><a name="l00773"></a><span class="lineno">  773</span>&#160;  <span class="comment">// Eq. (36)-(37)</span></div>
<div class="line"><a name="l00774"></a><span class="lineno">  774</span>&#160;  <span class="keyword">const</span> Scalar src_var = src_demean.rowwise ().squaredNorm ().sum () * one_over_n;</div>
<div class="line"><a name="l00775"></a><span class="lineno">  775</span>&#160; </div>
<div class="line"><a name="l00776"></a><span class="lineno">  776</span>&#160;  <span class="comment">// Eq. (38)</span></div>
<div class="line"><a name="l00777"></a><span class="lineno">  777</span>&#160;  <span class="keyword">const</span> MatrixType sigma (one_over_n * dst_demean * src_demean.transpose ());</div>
<div class="line"><a name="l00778"></a><span class="lineno">  778</span>&#160; </div>
<div class="line"><a name="l00779"></a><span class="lineno">  779</span>&#160;  Eigen::JacobiSVD&lt;MatrixType&gt; svd (sigma, Eigen::ComputeFullU | Eigen::ComputeFullV);</div>
<div class="line"><a name="l00780"></a><span class="lineno">  780</span>&#160; </div>
<div class="line"><a name="l00781"></a><span class="lineno">  781</span>&#160;  <span class="comment">// Initialize the resulting transformation with an identity matrix...</span></div>
<div class="line"><a name="l00782"></a><span class="lineno">  782</span>&#160;  TransformationMatrixType Rt = TransformationMatrixType::Identity (m + 1, m + 1);</div>
<div class="line"><a name="l00783"></a><span class="lineno">  783</span>&#160; </div>
<div class="line"><a name="l00784"></a><span class="lineno">  784</span>&#160;  <span class="comment">// Eq. (39)</span></div>
<div class="line"><a name="l00785"></a><span class="lineno">  785</span>&#160;  VectorType S = VectorType::Ones (m);</div>
<div class="line"><a name="l00786"></a><span class="lineno">  786</span>&#160; </div>
<div class="line"><a name="l00787"></a><span class="lineno">  787</span>&#160;  <span class="keywordflow">if</span>  ( svd.matrixU ().determinant () * svd.matrixV ().determinant () &lt; 0 )</div>
<div class="line"><a name="l00788"></a><span class="lineno">  788</span>&#160;    S (m - 1) = -1;</div>
<div class="line"><a name="l00789"></a><span class="lineno">  789</span>&#160; </div>
<div class="line"><a name="l00790"></a><span class="lineno">  790</span>&#160;  <span class="comment">// Eq. (40) and (43)</span></div>
<div class="line"><a name="l00791"></a><span class="lineno">  791</span>&#160;  Rt.block (0,0,m,m).noalias () = svd.matrixU () * S.asDiagonal () * svd.matrixV ().transpose ();</div>
<div class="line"><a name="l00792"></a><span class="lineno">  792</span>&#160; </div>
<div class="line"><a name="l00793"></a><span class="lineno">  793</span>&#160;  <span class="keywordflow">if</span> (with_scaling)</div>
<div class="line"><a name="l00794"></a><span class="lineno">  794</span>&#160;  {</div>
<div class="line"><a name="l00795"></a><span class="lineno">  795</span>&#160;    <span class="comment">// Eq. (42)</span></div>
<div class="line"><a name="l00796"></a><span class="lineno">  796</span>&#160;    <span class="keyword">const</span> Scalar c = Scalar (1)/ src_var * svd.singularValues ().dot (S);</div>
<div class="line"><a name="l00797"></a><span class="lineno">  797</span>&#160; </div>
<div class="line"><a name="l00798"></a><span class="lineno">  798</span>&#160;    <span class="comment">// Eq. (41)</span></div>
<div class="line"><a name="l00799"></a><span class="lineno">  799</span>&#160;    Rt.col (m).head (m) = dst_mean;</div>
<div class="line"><a name="l00800"></a><span class="lineno">  800</span>&#160;    Rt.col (m).head (m).noalias () -= c * Rt.topLeftCorner (m, m) * src_mean;</div>
<div class="line"><a name="l00801"></a><span class="lineno">  801</span>&#160;    Rt.block (0, 0, m, m) *= c;</div>
<div class="line"><a name="l00802"></a><span class="lineno">  802</span>&#160;  }</div>
<div class="line"><a name="l00803"></a><span class="lineno">  803</span>&#160;  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00804"></a><span class="lineno">  804</span>&#160;  {</div>
<div class="line"><a name="l00805"></a><span class="lineno">  805</span>&#160;    Rt.col (m).head (m) = dst_mean;</div>
<div class="line"><a name="l00806"></a><span class="lineno">  806</span>&#160;    Rt.col (m).head (m).noalias () -= Rt.topLeftCorner (m, m) * src_mean;</div>
<div class="line"><a name="l00807"></a><span class="lineno">  807</span>&#160;  }</div>
<div class="line"><a name="l00808"></a><span class="lineno">  808</span>&#160; </div>
<div class="line"><a name="l00809"></a><span class="lineno">  809</span>&#160;  <span class="keywordflow">return</span> (Rt);</div>
<div class="line"><a name="l00810"></a><span class="lineno">  810</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00811"></a><span class="lineno">  811</span>&#160;}</div>
<div class="line"><a name="l00812"></a><span class="lineno">  812</span>&#160; </div>
<div class="line"><a name="l00814"></a><span class="lineno">  814</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt; <span class="keywordtype">bool</span></div>
<div class="line"><a name="l00815"></a><span class="lineno">  815</span>&#160;pcl::transformLine (<span class="keyword">const</span> Eigen::Matrix&lt;Scalar, Eigen::Dynamic, 1&gt; &amp;line_in,</div>
<div class="line"><a name="l00816"></a><span class="lineno">  816</span>&#160;                          Eigen::Matrix&lt;Scalar, Eigen::Dynamic, 1&gt; &amp;line_out,</div>
<div class="line"><a name="l00817"></a><span class="lineno">  817</span>&#160;                    <span class="keyword">const</span> Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt; &amp;transformation)</div>
<div class="line"><a name="l00818"></a><span class="lineno">  818</span>&#160;{</div>
<div class="line"><a name="l00819"></a><span class="lineno">  819</span>&#160;  <span class="keywordflow">if</span> (line_in.innerSize () != 6 || line_out.innerSize () != 6)</div>
<div class="line"><a name="l00820"></a><span class="lineno">  820</span>&#160;  {</div>
<div class="line"><a name="l00821"></a><span class="lineno">  821</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;transformLine: lines size != 6\n&quot;</span>);</div>
<div class="line"><a name="l00822"></a><span class="lineno">  822</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00823"></a><span class="lineno">  823</span>&#160;  }</div>
<div class="line"><a name="l00824"></a><span class="lineno">  824</span>&#160; </div>
<div class="line"><a name="l00825"></a><span class="lineno">  825</span>&#160;  Eigen::Matrix&lt;Scalar, 3, 1&gt; point, vector;</div>
<div class="line"><a name="l00826"></a><span class="lineno">  826</span>&#160;  point &lt;&lt; line_in.template head&lt;3&gt; ();</div>
<div class="line"><a name="l00827"></a><span class="lineno">  827</span>&#160;  vector &lt;&lt; line_out.template tail&lt;3&gt; ();</div>
<div class="line"><a name="l00828"></a><span class="lineno">  828</span>&#160; </div>
<div class="line"><a name="l00829"></a><span class="lineno">  829</span>&#160;  <a class="code" href="group__common.html#ga1bd2c5ea1258af3a45483dd1341aa429">pcl::transformPoint</a> (point, point, transformation);</div>
<div class="line"><a name="l00830"></a><span class="lineno">  830</span>&#160;  pcl::transformVector (vector, vector, transformation);</div>
<div class="line"><a name="l00831"></a><span class="lineno">  831</span>&#160;  line_out &lt;&lt; point, vector;</div>
<div class="line"><a name="l00832"></a><span class="lineno">  832</span>&#160;  <span class="keywordflow">return</span> (<span class="keyword">true</span>);</div>
<div class="line"><a name="l00833"></a><span class="lineno">  833</span>&#160;}</div>
<div class="line"><a name="l00834"></a><span class="lineno">  834</span>&#160; </div>
<div class="line"><a name="l00836"></a><span class="lineno">  836</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00837"></a><span class="lineno">  837</span>&#160;pcl::transformPlane (<span class="keyword">const</span> Eigen::Matrix&lt;Scalar, 4, 1&gt; &amp;plane_in,</div>
<div class="line"><a name="l00838"></a><span class="lineno">  838</span>&#160;                           Eigen::Matrix&lt;Scalar, 4, 1&gt; &amp;plane_out,</div>
<div class="line"><a name="l00839"></a><span class="lineno">  839</span>&#160;                     <span class="keyword">const</span> Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt; &amp;transformation)</div>
<div class="line"><a name="l00840"></a><span class="lineno">  840</span>&#160;{</div>
<div class="line"><a name="l00841"></a><span class="lineno">  841</span>&#160;  Eigen::Hyperplane &lt; Scalar, 3 &gt; plane;</div>
<div class="line"><a name="l00842"></a><span class="lineno">  842</span>&#160;  plane.coeffs () &lt;&lt; plane_in;</div>
<div class="line"><a name="l00843"></a><span class="lineno">  843</span>&#160;  plane.transform (transformation);</div>
<div class="line"><a name="l00844"></a><span class="lineno">  844</span>&#160;  plane_out &lt;&lt; plane.coeffs ();</div>
<div class="line"><a name="l00845"></a><span class="lineno">  845</span>&#160;}</div>
<div class="line"><a name="l00846"></a><span class="lineno">  846</span>&#160; </div>
<div class="line"><a name="l00848"></a><span class="lineno">  848</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt; <span class="keywordtype">void</span></div>
<div class="line"><a name="l00849"></a><span class="lineno">  849</span>&#160;pcl::transformPlane (<span class="keyword">const</span> pcl::ModelCoefficients::Ptr plane_in,</div>
<div class="line"><a name="l00850"></a><span class="lineno">  850</span>&#160;                           pcl::ModelCoefficients::Ptr plane_out,</div>
<div class="line"><a name="l00851"></a><span class="lineno">  851</span>&#160;                     <span class="keyword">const</span> Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt; &amp;transformation)</div>
<div class="line"><a name="l00852"></a><span class="lineno">  852</span>&#160;{</div>
<div class="line"><a name="l00853"></a><span class="lineno">  853</span>&#160;  Eigen::Matrix &lt; Scalar, 4, 1 &gt; v_plane_in (std::vector &lt; Scalar &gt; (plane_in-&gt;values.begin (), plane_in-&gt;values.end ()).data ());</div>
<div class="line"><a name="l00854"></a><span class="lineno">  854</span>&#160;  pcl::transformPlane (v_plane_in, v_plane_in, transformation);</div>
<div class="line"><a name="l00855"></a><span class="lineno">  855</span>&#160;  plane_out-&gt;values.resize (4);</div>
<div class="line"><a name="l00856"></a><span class="lineno">  856</span>&#160;  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; 4; i++)</div>
<div class="line"><a name="l00857"></a><span class="lineno">  857</span>&#160;    plane_in-&gt;values[i] = v_plane_in[i];</div>
<div class="line"><a name="l00858"></a><span class="lineno">  858</span>&#160;}</div>
<div class="line"><a name="l00859"></a><span class="lineno">  859</span>&#160; </div>
<div class="line"><a name="l00861"></a><span class="lineno">  861</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt; <span class="keywordtype">bool</span></div>
<div class="line"><a name="l00862"></a><span class="lineno">  862</span>&#160;pcl::checkCoordinateSystem (<span class="keyword">const</span> Eigen::Matrix&lt;Scalar, Eigen::Dynamic, 1&gt; &amp;line_x,</div>
<div class="line"><a name="l00863"></a><span class="lineno">  863</span>&#160;                            <span class="keyword">const</span> Eigen::Matrix&lt;Scalar, Eigen::Dynamic, 1&gt; &amp;line_y,</div>
<div class="line"><a name="l00864"></a><span class="lineno">  864</span>&#160;                            <span class="keyword">const</span> Scalar norm_limit,</div>
<div class="line"><a name="l00865"></a><span class="lineno">  865</span>&#160;                            <span class="keyword">const</span> Scalar dot_limit)</div>
<div class="line"><a name="l00866"></a><span class="lineno">  866</span>&#160;{</div>
<div class="line"><a name="l00867"></a><span class="lineno">  867</span>&#160;  <span class="keywordflow">if</span> (line_x.innerSize () != 6 || line_y.innerSize () != 6)</div>
<div class="line"><a name="l00868"></a><span class="lineno">  868</span>&#160;  {</div>
<div class="line"><a name="l00869"></a><span class="lineno">  869</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;checkCoordinateSystem: lines size != 6\n&quot;</span>);</div>
<div class="line"><a name="l00870"></a><span class="lineno">  870</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00871"></a><span class="lineno">  871</span>&#160;  }</div>
<div class="line"><a name="l00872"></a><span class="lineno">  872</span>&#160; </div>
<div class="line"><a name="l00873"></a><span class="lineno">  873</span>&#160;  <span class="keywordflow">if</span> (line_x.template head&lt;3&gt; () != line_y.template head&lt;3&gt; ())</div>
<div class="line"><a name="l00874"></a><span class="lineno">  874</span>&#160;  {</div>
<div class="line"><a name="l00875"></a><span class="lineno">  875</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;checkCoorZdinateSystem: vector origins are different !\n&quot;</span>);</div>
<div class="line"><a name="l00876"></a><span class="lineno">  876</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00877"></a><span class="lineno">  877</span>&#160;  }</div>
<div class="line"><a name="l00878"></a><span class="lineno">  878</span>&#160; </div>
<div class="line"><a name="l00879"></a><span class="lineno">  879</span>&#160;  <span class="comment">// Make a copy of vector directions</span></div>
<div class="line"><a name="l00880"></a><span class="lineno">  880</span>&#160;  <span class="comment">// X^Y = Z | Y^Z = X | Z^X = Y</span></div>
<div class="line"><a name="l00881"></a><span class="lineno">  881</span>&#160;  Eigen::Matrix&lt;Scalar, 3, 1&gt; v_line_x (line_x.template tail&lt;3&gt; ()),</div>
<div class="line"><a name="l00882"></a><span class="lineno">  882</span>&#160;                              v_line_y (line_y.template tail&lt;3&gt; ()),</div>
<div class="line"><a name="l00883"></a><span class="lineno">  883</span>&#160;                              v_line_z (v_line_x.cross (v_line_y));</div>
<div class="line"><a name="l00884"></a><span class="lineno">  884</span>&#160; </div>
<div class="line"><a name="l00885"></a><span class="lineno">  885</span>&#160;  <span class="comment">// Check vectors norms</span></div>
<div class="line"><a name="l00886"></a><span class="lineno">  886</span>&#160;  <span class="keywordflow">if</span> (v_line_x.norm () &lt; 1 - norm_limit || v_line_x.norm () &gt; 1 + norm_limit)</div>
<div class="line"><a name="l00887"></a><span class="lineno">  887</span>&#160;  {</div>
<div class="line"><a name="l00888"></a><span class="lineno">  888</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;checkCoordinateSystem: line_x norm %d != 1\n&quot;</span>, v_line_x.norm ());</div>
<div class="line"><a name="l00889"></a><span class="lineno">  889</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00890"></a><span class="lineno">  890</span>&#160;  }</div>
<div class="line"><a name="l00891"></a><span class="lineno">  891</span>&#160; </div>
<div class="line"><a name="l00892"></a><span class="lineno">  892</span>&#160;  <span class="keywordflow">if</span> (v_line_y.norm () &lt; 1 - norm_limit || v_line_y.norm () &gt; 1 + norm_limit)</div>
<div class="line"><a name="l00893"></a><span class="lineno">  893</span>&#160;  {</div>
<div class="line"><a name="l00894"></a><span class="lineno">  894</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;checkCoordinateSystem: line_y norm %d != 1\n&quot;</span>, v_line_y.norm ());</div>
<div class="line"><a name="l00895"></a><span class="lineno">  895</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00896"></a><span class="lineno">  896</span>&#160;  }</div>
<div class="line"><a name="l00897"></a><span class="lineno">  897</span>&#160; </div>
<div class="line"><a name="l00898"></a><span class="lineno">  898</span>&#160;  <span class="keywordflow">if</span> (v_line_z.norm () &lt; 1 - norm_limit || v_line_z.norm () &gt; 1 + norm_limit)</div>
<div class="line"><a name="l00899"></a><span class="lineno">  899</span>&#160;  {</div>
<div class="line"><a name="l00900"></a><span class="lineno">  900</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;checkCoordinateSystem: line_z norm %d != 1\n&quot;</span>, v_line_z.norm ());</div>
<div class="line"><a name="l00901"></a><span class="lineno">  901</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00902"></a><span class="lineno">  902</span>&#160;  }</div>
<div class="line"><a name="l00903"></a><span class="lineno">  903</span>&#160; </div>
<div class="line"><a name="l00904"></a><span class="lineno">  904</span>&#160;  <span class="comment">// Check vectors perendicularity</span></div>
<div class="line"><a name="l00905"></a><span class="lineno">  905</span>&#160;  <span class="keywordflow">if</span> (std::abs (v_line_x.dot (v_line_y)) &gt; dot_limit)</div>
<div class="line"><a name="l00906"></a><span class="lineno">  906</span>&#160;  {</div>
<div class="line"><a name="l00907"></a><span class="lineno">  907</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;checkCSAxis: line_x dot line_y %e =  &gt; %e\n&quot;</span>, v_line_x.dot (v_line_y), dot_limit);</div>
<div class="line"><a name="l00908"></a><span class="lineno">  908</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00909"></a><span class="lineno">  909</span>&#160;  }</div>
<div class="line"><a name="l00910"></a><span class="lineno">  910</span>&#160; </div>
<div class="line"><a name="l00911"></a><span class="lineno">  911</span>&#160;  <span class="keywordflow">if</span> (std::abs (v_line_x.dot (v_line_z)) &gt; dot_limit)</div>
<div class="line"><a name="l00912"></a><span class="lineno">  912</span>&#160;  {</div>
<div class="line"><a name="l00913"></a><span class="lineno">  913</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;checkCSAxis: line_x dot line_z = %e &gt; %e\n&quot;</span>, v_line_x.dot (v_line_z), dot_limit);</div>
<div class="line"><a name="l00914"></a><span class="lineno">  914</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00915"></a><span class="lineno">  915</span>&#160;  }</div>
<div class="line"><a name="l00916"></a><span class="lineno">  916</span>&#160; </div>
<div class="line"><a name="l00917"></a><span class="lineno">  917</span>&#160;  <span class="keywordflow">if</span> (std::abs (v_line_y.dot (v_line_z)) &gt; dot_limit)</div>
<div class="line"><a name="l00918"></a><span class="lineno">  918</span>&#160;  {</div>
<div class="line"><a name="l00919"></a><span class="lineno">  919</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;checkCSAxis: line_y dot line_z = %e &gt; %e\n&quot;</span>, v_line_y.dot (v_line_z), dot_limit);</div>
<div class="line"><a name="l00920"></a><span class="lineno">  920</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00921"></a><span class="lineno">  921</span>&#160;  }</div>
<div class="line"><a name="l00922"></a><span class="lineno">  922</span>&#160; </div>
<div class="line"><a name="l00923"></a><span class="lineno">  923</span>&#160;  <span class="keywordflow">return</span> (<span class="keyword">true</span>);</div>
<div class="line"><a name="l00924"></a><span class="lineno">  924</span>&#160;}</div>
<div class="line"><a name="l00925"></a><span class="lineno">  925</span>&#160; </div>
<div class="line"><a name="l00927"></a><span class="lineno">  927</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> Scalar&gt; <span class="keywordtype">bool</span></div>
<div class="line"><a name="l00928"></a><span class="lineno">  928</span>&#160;pcl::transformBetween2CoordinateSystems (<span class="keyword">const</span> Eigen::Matrix&lt;Scalar, Eigen::Dynamic, 1&gt; from_line_x,</div>
<div class="line"><a name="l00929"></a><span class="lineno">  929</span>&#160;                                         <span class="keyword">const</span> Eigen::Matrix&lt;Scalar, Eigen::Dynamic, 1&gt; from_line_y,</div>
<div class="line"><a name="l00930"></a><span class="lineno">  930</span>&#160;                                         <span class="keyword">const</span> Eigen::Matrix&lt;Scalar, Eigen::Dynamic, 1&gt; to_line_x,</div>
<div class="line"><a name="l00931"></a><span class="lineno">  931</span>&#160;                                         <span class="keyword">const</span> Eigen::Matrix&lt;Scalar, Eigen::Dynamic, 1&gt; to_line_y,</div>
<div class="line"><a name="l00932"></a><span class="lineno">  932</span>&#160;                                         Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt; &amp;transformation)</div>
<div class="line"><a name="l00933"></a><span class="lineno">  933</span>&#160;{</div>
<div class="line"><a name="l00934"></a><span class="lineno">  934</span>&#160;  <span class="keywordflow">if</span> (from_line_x.innerSize () != 6 || from_line_y.innerSize () != 6 || to_line_x.innerSize () != 6 || to_line_y.innerSize () != 6)</div>
<div class="line"><a name="l00935"></a><span class="lineno">  935</span>&#160;  {</div>
<div class="line"><a name="l00936"></a><span class="lineno">  936</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;transformBetween2CoordinateSystems: lines size != 6\n&quot;</span>);</div>
<div class="line"><a name="l00937"></a><span class="lineno">  937</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00938"></a><span class="lineno">  938</span>&#160;  }</div>
<div class="line"><a name="l00939"></a><span class="lineno">  939</span>&#160; </div>
<div class="line"><a name="l00940"></a><span class="lineno">  940</span>&#160;  <span class="comment">// Check if coordinate systems are valid</span></div>
<div class="line"><a name="l00941"></a><span class="lineno">  941</span>&#160;  <span class="keywordflow">if</span> (!pcl::checkCoordinateSystem (from_line_x, from_line_y) || !pcl::checkCoordinateSystem (to_line_x, to_line_y))</div>
<div class="line"><a name="l00942"></a><span class="lineno">  942</span>&#160;  {</div>
<div class="line"><a name="l00943"></a><span class="lineno">  943</span>&#160;    PCL_DEBUG (<span class="stringliteral">&quot;transformBetween2CoordinateSystems: coordinate systems invalid !\n&quot;</span>);</div>
<div class="line"><a name="l00944"></a><span class="lineno">  944</span>&#160;    <span class="keywordflow">return</span> (<span class="keyword">false</span>);</div>
<div class="line"><a name="l00945"></a><span class="lineno">  945</span>&#160;  }</div>
<div class="line"><a name="l00946"></a><span class="lineno">  946</span>&#160; </div>
<div class="line"><a name="l00947"></a><span class="lineno">  947</span>&#160;  <span class="comment">// Convert lines into Vector3 :</span></div>
<div class="line"><a name="l00948"></a><span class="lineno">  948</span>&#160;  Eigen::Matrix&lt;Scalar, 3, 1&gt; fr0 (from_line_x.template head&lt;3&gt;()),</div>
<div class="line"><a name="l00949"></a><span class="lineno">  949</span>&#160;                              fr1 (from_line_x.template head&lt;3&gt;() + from_line_x.template tail&lt;3&gt;()),</div>
<div class="line"><a name="l00950"></a><span class="lineno">  950</span>&#160;                              fr2 (from_line_y.template head&lt;3&gt;() + from_line_y.template tail&lt;3&gt;()),</div>
<div class="line"><a name="l00951"></a><span class="lineno">  951</span>&#160; </div>
<div class="line"><a name="l00952"></a><span class="lineno">  952</span>&#160;                              to0 (to_line_x.template head&lt;3&gt;()),</div>
<div class="line"><a name="l00953"></a><span class="lineno">  953</span>&#160;                              to1 (to_line_x.template head&lt;3&gt;() + to_line_x.template tail&lt;3&gt;()),</div>
<div class="line"><a name="l00954"></a><span class="lineno">  954</span>&#160;                              to2 (to_line_y.template head&lt;3&gt;() + to_line_y.template tail&lt;3&gt;());</div>
<div class="line"><a name="l00955"></a><span class="lineno">  955</span>&#160; </div>
<div class="line"><a name="l00956"></a><span class="lineno">  956</span>&#160;  <span class="comment">// Code is inspired from http://stackoverflow.com/a/15277421/1816078</span></div>
<div class="line"><a name="l00957"></a><span class="lineno">  957</span>&#160;  <span class="comment">// Define matrices and points :</span></div>
<div class="line"><a name="l00958"></a><span class="lineno">  958</span>&#160;  Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt; T2, T3 = Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt;::Identity ();</div>
<div class="line"><a name="l00959"></a><span class="lineno">  959</span>&#160;  Eigen::Matrix&lt;Scalar, 3, 1&gt; x1, y1, z1, x2, y2, z2;</div>
<div class="line"><a name="l00960"></a><span class="lineno">  960</span>&#160; </div>
<div class="line"><a name="l00961"></a><span class="lineno">  961</span>&#160;  <span class="comment">// Axes of the coordinate system &quot;fr&quot;</span></div>
<div class="line"><a name="l00962"></a><span class="lineno">  962</span>&#160;  x1 = (fr1 - fr0).normalized ();  <span class="comment">// the versor (unitary vector) of the (fr1-fr0) axis vector</span></div>
<div class="line"><a name="l00963"></a><span class="lineno">  963</span>&#160;  y1 = (fr2 - fr0).normalized ();</div>
<div class="line"><a name="l00964"></a><span class="lineno">  964</span>&#160; </div>
<div class="line"><a name="l00965"></a><span class="lineno">  965</span>&#160;  <span class="comment">// Axes of the coordinate system &quot;to&quot;</span></div>
<div class="line"><a name="l00966"></a><span class="lineno">  966</span>&#160;  x2 = (to1 - to0).normalized ();</div>
<div class="line"><a name="l00967"></a><span class="lineno">  967</span>&#160;  y2 = (to2 - to0).normalized ();</div>
<div class="line"><a name="l00968"></a><span class="lineno">  968</span>&#160; </div>
<div class="line"><a name="l00969"></a><span class="lineno">  969</span>&#160;  <span class="comment">// Transform from CS1 to CS2</span></div>
<div class="line"><a name="l00970"></a><span class="lineno">  970</span>&#160;  <span class="comment">// Note: if fr0 == (0,0,0) --&gt; CS1 == CS2 --&gt; T2 = Identity</span></div>
<div class="line"><a name="l00971"></a><span class="lineno">  971</span>&#160;  T2.linear () &lt;&lt; x1, y1, x1.cross (y1);</div>
<div class="line"><a name="l00972"></a><span class="lineno">  972</span>&#160; </div>
<div class="line"><a name="l00973"></a><span class="lineno">  973</span>&#160;  <span class="comment">// Transform from CS1 to CS3</span></div>
<div class="line"><a name="l00974"></a><span class="lineno">  974</span>&#160;  T3.linear () &lt;&lt; x2, y2, x2.cross (y2);</div>
<div class="line"><a name="l00975"></a><span class="lineno">  975</span>&#160; </div>
<div class="line"><a name="l00976"></a><span class="lineno">  976</span>&#160;  <span class="comment">// Identity matrix = transform to CS2 to CS3</span></div>
<div class="line"><a name="l00977"></a><span class="lineno">  977</span>&#160;  <span class="comment">// Note: if CS1 == CS2 --&gt; transformation = T3</span></div>
<div class="line"><a name="l00978"></a><span class="lineno">  978</span>&#160;  transformation = Eigen::Transform&lt;Scalar, 3, Eigen::Affine&gt;::Identity ();</div>
<div class="line"><a name="l00979"></a><span class="lineno">  979</span>&#160;  transformation.linear () = T3.linear () * T2.linear ().inverse ();</div>
<div class="line"><a name="l00980"></a><span class="lineno">  980</span>&#160;  transformation.translation () = to0 - (transformation.linear () * fr0);</div>
<div class="line"><a name="l00981"></a><span class="lineno">  981</span>&#160;  <span class="keywordflow">return</span> (<span class="keyword">true</span>);</div>
<div class="line"><a name="l00982"></a><span class="lineno">  982</span>&#160;}</div>
<div class="line"><a name="l00983"></a><span class="lineno">  983</span>&#160; </div>
<div class="line"><a name="l00984"></a><span class="lineno">  984</span>&#160;<span class="preprocessor">#endif  </span><span class="comment">//PCL_COMMON_EIGEN_IMPL_HPP_</span></div>
<div class="line"><a name="l00985"></a><span class="lineno">  985</span>&#160; </div>
<div class="ttc" id="agroup__common_html_ga11c9b186d04d2e8a868e058473214622"><div class="ttname"><a href="group__common.html#ga11c9b186d04d2e8a868e058473214622">pcl::computeCorrespondingEigenVector</a></div><div class="ttdeci">void computeCorrespondingEigenVector(const Matrix &amp;mat, const typename Matrix::Scalar &amp;eigenvalue, Vector &amp;eigenvector)</div><div class="ttdoc">determines the corresponding eigenvector to the given eigenvalue of the symmetric positive semi defin...</div><div class="ttdef"><b>Definition:</b> eigen.hpp:219</div></div>
<div class="ttc" id="agroup__common_html_ga1bd2c5ea1258af3a45483dd1341aa429"><div class="ttname"><a href="group__common.html#ga1bd2c5ea1258af3a45483dd1341aa429">pcl::transformPoint</a></div><div class="ttdeci">PointT transformPoint(const PointT &amp;point, const Eigen::Transform&lt; Scalar, 3, Eigen::Affine &gt; &amp;transform)</div><div class="ttdoc">Transform a point with members x,y,z</div><div class="ttdef"><b>Definition:</b> transforms.hpp:315</div></div>
<div class="ttc" id="agroup__common_html_ga3e52d439a979e71096f4dd50f1298f32"><div class="ttname"><a href="group__common.html#ga3e52d439a979e71096f4dd50f1298f32">pcl::getTranslationAndEulerAngles</a></div><div class="ttdeci">void getTranslationAndEulerAngles(const Eigen::Transform&lt; Scalar, 3, Eigen::Affine &gt; &amp;t, Scalar &amp;x, Scalar &amp;y, Scalar &amp;z, Scalar &amp;roll, Scalar &amp;pitch, Scalar &amp;yaw)</div><div class="ttdef"><b>Definition:</b> eigen.hpp:673</div></div>
<div class="ttc" id="agroup__common_html_ga4375e99ec2ae368eec9379f506568611"><div class="ttname"><a href="group__common.html#ga4375e99ec2ae368eec9379f506568611">pcl::getTransformationFromTwoUnitVectorsAndOrigin</a></div><div class="ttdeci">void getTransformationFromTwoUnitVectorsAndOrigin(const Eigen::Vector3f &amp;y_direction, const Eigen::Vector3f &amp;z_axis, const Eigen::Vector3f &amp;origin, Eigen::Affine3f &amp;transformation)</div><div class="ttdoc">Get the transformation that will translate orign to (0,0,0) and rotate z_axis into (0,...</div><div class="ttdef"><b>Definition:</b> eigen.hpp:652</div></div>
<div class="ttc" id="agroup__common_html_ga44d0048ba1efd11359011eb47f6c92fa"><div class="ttname"><a href="group__common.html#ga44d0048ba1efd11359011eb47f6c92fa">pcl::determinant3x3Matrix</a></div><div class="ttdeci">Matrix::Scalar determinant3x3Matrix(const Matrix &amp;matrix)</div><div class="ttdoc">Calculate the determinant of a 3x3 matrix.</div><div class="ttdef"><b>Definition:</b> eigen.hpp:572</div></div>
<div class="ttc" id="agroup__common_html_ga503f55a565c260660c6ac0461f17fa8f"><div class="ttname"><a href="group__common.html#ga503f55a565c260660c6ac0461f17fa8f">pcl::invert3x3SymMatrix</a></div><div class="ttdeci">Matrix::Scalar invert3x3SymMatrix(const Matrix &amp;matrix, Matrix &amp;inverse)</div><div class="ttdoc">Calculate the inverse of a 3x3 symmetric matrix.</div><div class="ttdef"><b>Definition:</b> eigen.hpp:504</div></div>
<div class="ttc" id="agroup__common_html_ga5281205532955d384c8aa22ff4ff5e80"><div class="ttname"><a href="group__common.html#ga5281205532955d384c8aa22ff4ff5e80">pcl::loadBinary</a></div><div class="ttdeci">void loadBinary(Eigen::MatrixBase&lt; Derived &gt; const &amp;matrix, std::istream &amp;file)</div><div class="ttdoc">Read a matrix from an input stream</div><div class="ttdef"><b>Definition:</b> eigen.hpp:717</div></div>
<div class="ttc" id="agroup__common_html_ga5cc746d1fd72f99fee462ed1a9e4abea"><div class="ttname"><a href="group__common.html#ga5cc746d1fd72f99fee462ed1a9e4abea">pcl::getTransformation</a></div><div class="ttdeci">void getTransformation(Scalar x, Scalar y, Scalar z, Scalar roll, Scalar pitch, Scalar yaw, Eigen::Transform&lt; Scalar, 3, Eigen::Affine &gt; &amp;t)</div><div class="ttdoc">Create a transformation from the given translation and Euler angles (XYZ-convention)</div><div class="ttdef"><b>Definition:</b> eigen.hpp:687</div></div>
<div class="ttc" id="agroup__common_html_ga637da495fec59c1c1d186aa6e3bac15b"><div class="ttname"><a href="group__common.html#ga637da495fec59c1c1d186aa6e3bac15b">pcl::getEulerAngles</a></div><div class="ttdeci">void getEulerAngles(const Eigen::Transform&lt; Scalar, 3, Eigen::Affine &gt; &amp;t, Scalar &amp;roll, Scalar &amp;pitch, Scalar &amp;yaw)</div><div class="ttdoc">Extract the Euler angles (XYZ-convention) from the given transformation</div><div class="ttdef"><b>Definition:</b> eigen.hpp:664</div></div>
<div class="ttc" id="agroup__common_html_ga72970b7435480c0c1827c8e74bc1d605"><div class="ttname"><a href="group__common.html#ga72970b7435480c0c1827c8e74bc1d605">pcl::eigen22</a></div><div class="ttdeci">void eigen22(const Matrix &amp;mat, typename Matrix::Scalar &amp;eigenvalue, Vector &amp;eigenvector)</div><div class="ttdoc">determine the smallest eigenvalue and its corresponding eigenvector</div><div class="ttdef"><b>Definition:</b> eigen.hpp:126</div></div>
<div class="ttc" id="agroup__common_html_ga7d1f523f342ff69277f23ea9f02fc5a6"><div class="ttname"><a href="group__common.html#ga7d1f523f342ff69277f23ea9f02fc5a6">pcl::getTransformationFromTwoUnitVectors</a></div><div class="ttdeci">void getTransformationFromTwoUnitVectors(const Eigen::Vector3f &amp;y_direction, const Eigen::Vector3f &amp;z_axis, Eigen::Affine3f &amp;transformation)</div><div class="ttdoc">Get the unique 3D rotation that will rotate z_axis into (0,0,1) and y_direction into a vector with x=...</div><div class="ttdef"><b>Definition:</b> eigen.hpp:634</div></div>
<div class="ttc" id="agroup__common_html_ga8319aa7921bdc742a9d0f95458e9cfe0"><div class="ttname"><a href="group__common.html#ga8319aa7921bdc742a9d0f95458e9cfe0">pcl::getTransFromUnitVectorsXY</a></div><div class="ttdeci">void getTransFromUnitVectorsXY(const Eigen::Vector3f &amp;x_axis, const Eigen::Vector3f &amp;y_direction, Eigen::Affine3f &amp;transformation)</div><div class="ttdoc">Get the unique 3D rotation that will rotate x_axis into (1,0,0) and y_direction into a vector with z=...</div><div class="ttdef"><b>Definition:</b> eigen.hpp:608</div></div>
<div class="ttc" id="agroup__common_html_gabb12d1f85437aafb0a3ac12af5633400"><div class="ttname"><a href="group__common.html#gabb12d1f85437aafb0a3ac12af5633400">pcl::invert3x3Matrix</a></div><div class="ttdeci">Matrix::Scalar invert3x3Matrix(const Matrix &amp;matrix, Matrix &amp;inverse)</div><div class="ttdoc">Calculate the inverse of a general 3x3 matrix.</div><div class="ttdef"><b>Definition:</b> eigen.hpp:539</div></div>
<div class="ttc" id="agroup__common_html_gaca873868052e7d26efcf4b684a17bef2"><div class="ttname"><a href="group__common.html#gaca873868052e7d26efcf4b684a17bef2">pcl::eigen33</a></div><div class="ttdeci">void eigen33(const Matrix &amp;mat, typename Matrix::Scalar &amp;eigenvalue, Vector &amp;eigenvector)</div><div class="ttdoc">determines the eigenvector and eigenvalue of the smallest eigenvalue of the symmetric positive semi d...</div><div class="ttdef"><b>Definition:</b> eigen.hpp:251</div></div>
<div class="ttc" id="agroup__common_html_gacc18ebcacd806fd0c9336fe2f8b7208c"><div class="ttname"><a href="group__common.html#gacc18ebcacd806fd0c9336fe2f8b7208c">pcl::saveBinary</a></div><div class="ttdeci">void saveBinary(const Eigen::MatrixBase&lt; Derived &gt; &amp;matrix, std::ostream &amp;file)</div><div class="ttdoc">Write a matrix to an output stream</div><div class="ttdef"><b>Definition:</b> eigen.hpp:702</div></div>
<div class="ttc" id="agroup__common_html_gad09b0c9a50601f3ae20a7babfd9a8d2d"><div class="ttname"><a href="group__common.html#gad09b0c9a50601f3ae20a7babfd9a8d2d">pcl::invert2x2</a></div><div class="ttdeci">Matrix::Scalar invert2x2(const Matrix &amp;matrix, Matrix &amp;inverse)</div><div class="ttdoc">Calculate the inverse of a 2x2 matrix</div><div class="ttdef"><b>Definition:</b> eigen.hpp:485</div></div>
<div class="ttc" id="agroup__common_html_gaf457d33994792e63129de9709dcdf329"><div class="ttname"><a href="group__common.html#gaf457d33994792e63129de9709dcdf329">pcl::getTransFromUnitVectorsZY</a></div><div class="ttdeci">void getTransFromUnitVectorsZY(const Eigen::Vector3f &amp;z_axis, const Eigen::Vector3f &amp;y_direction, Eigen::Affine3f &amp;transformation)</div><div class="ttdoc">Get the unique 3D rotation that will rotate z_axis into (0,0,1) and y_direction into a vector with x=...</div><div class="ttdef"><b>Definition:</b> eigen.hpp:582</div></div>
</div><!-- fragment --></div><!-- contents -->
</div><!-- doc-content -->
<!-- start footer part -->
<div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
  <ul>
    <li class="navelem"><a class="el" href="dir_bdd9a5d540de89e9fe90efdfc6973a4f.html">common</a></li><li class="navelem"><a class="el" href="dir_11fbc4217d50ab21044e5ad6614aede5.html">include</a></li><li class="navelem"><a class="el" href="dir_39ef148c3cf3468c290ae8c03b3c03af.html">pcl</a></li><li class="navelem"><a class="el" href="dir_474708a720ff06817ce2c12e28baf137.html">common</a></li><li class="navelem"><a class="el" href="dir_c98c7570052243dd3cc27194f001d1db.html">impl</a></li><li class="navelem"><b>eigen.hpp</b></li>
    <li class="footer">制作者 <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.1 </li>
  </ul>
</div>
</body>
</html>
